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167 relations: Absolute difference, Aleksandrov–Rassias problem, Approach space, Augustin-Louis Cauchy, Baire space, Ball (mathematics), Banach fixed-point theorem, Banach space, Base (topology), Bijection, Bounded function, Bounded set, British Rail, Cambridge University Press, Cantor set, Category (mathematics), Category of metric spaces, Cauchy sequence, Cayley graph, Chebyshev distance, Classical Wiener space, Closed set, Closure (topology), Compact space, Complement (set theory), Complete metric space, Concave function, Connected space, Connectedness, Continuous function, Contraction mapping, Countable set, Countably compact space, Cover (topology), Curve, Cut-the-Knot, Dense set, Diagram (category theory), Diameter, Discrete space, Domain theory, Edit distance, Eduard Heine, Element (mathematics), Elliptic geometry, Enriched category, Equivalence relation, Euclidean distance, Euclidean space, European Mathematical Society, ..., Extended real number line, Felix Hausdorff, Field (mathematics), Finite set, First-countable space, Function (mathematics), Function space, Game theory, Geometric group theory, Glossary of Riemannian and metric geometry, Graph (discrete mathematics), Graph edit distance, Graph operations, Graph theory, Gromov–Hausdorff convergence, Hausdorff distance, Hausdorff space, Heine–Borel theorem, Heine–Cantor theorem, Helly metric, Hilbert space, Hilbert's fourth problem, Homeomorphism, Hyperbolic geometry, Hyperboloid model, Identity element, Identity of indiscernibles, If and only if, Image (mathematics), Infimum and supremum, Injective function, Interval (mathematics), Isometry, King (chess), Kuratowski convergence, Lebesgue measure, Lebesgue's number lemma, Levenshtein distance, Limit of a sequence, Lindelöf space, Line (geometry), Line segment, Lipschitz continuity, Locally compact space, Locally connected space, Mathematics, Matrix (mathematics), Maurice René Fréchet, Measure (mathematics), Metric (mathematics), Metric map, Metric signature, Metric tensor, Metric tree, Metrization theorem, Monoidal category, Morphism, Nati Linial, Neighbourhood (mathematics), Norm (mathematics), Normal space, Normed vector space, Open set, Ordered pair, Paracompact space, Partially ordered set, Partition of unity, Pavel Alexandrov, Pavel Urysohn, Positive real numbers, Product metric, Product topology, Pseudometric space, Quasi-isometry, Rank (linear algebra), Rational number, Real number, Riemannian manifold, Second-countable space, Separable space, Sequence, Sequential space, Sequentially compact space, Set (mathematics), Sign (mathematics), Simply connected space, SNCF, Space (mathematics), Special relativity, Sphere, String (computer science), Subadditivity, Subsequence, Subset, Surjective function, Symmetric function, T-theory, Taxicab geometry, Tensor product, Three-dimensional space, Tietze extension theorem, Tight span, Topological property, Topological space, Totally bounded space, Triangle inequality, Tychonoff space, Ultrametric space, Uniform continuity, Uniform isomorphism, Uniform norm, Uniform space, Universal property, Velocity, Word metric, Yuri Burago, (ε, δ)-definition of limit. Expand index (117 more) »
Absolute difference
The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference.
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Aleksandrov–Rassias problem
The theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932.
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Approach space
In topology, approach spaces are a generalization of metric spaces, based on point-to-set distances, instead of point-to-point distances.
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Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.
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Baire space
In mathematics, a Baire space is a topological space such that every intersection of a countable collection of open dense sets in the space is also dense.
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Ball (mathematics)
In mathematics, a ball is the space bounded by a sphere.
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Banach fixed-point theorem
In mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contraction mapping principle) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Base (topology)
In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.We are using a convention that the union of empty collection of sets is the empty set.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Bounded function
In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded.
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Bounded set
In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size.
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British Rail
British Railways (BR), which from 1965 traded as British Rail, was the state-owned company that operated most of the rail transport in Great Britain between 1948 and 1997.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cantor set
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.
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Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
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Category of metric spaces
In category-theoretic mathematics, Met is a category that has metric spaces as its objects and metric maps (continuous functions between metric spaces that do not increase any pairwise distance) as its morphisms.
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Cauchy sequence
In mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
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Cayley graph
In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group.
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Chebyshev distance
In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension.
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Classical Wiener space
In mathematics, classical Wiener space is the collection of all continuous functions on a given domain (usually a sub-interval of the real line), taking values in a metric space (usually n-dimensional Euclidean space).
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Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
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Closure (topology)
In mathematics, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure can be thought of as all the points that are either in S or "near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
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Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
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Complement (set theory)
In set theory, the complement of a set refers to elements not in.
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Complete metric space
In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary).
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Concave function
In mathematics, a concave function is the negative of a convex function.
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint nonempty open subsets.
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Connectedness
In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece".
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Contraction mapping
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M,d) is a function f from M to itself, with the property that there is some nonnegative real number 0\leq k such that for all x and y in M, The smallest such value of k is called the Lipschitz constant of f. Contractive maps are sometimes called Lipschitzian maps.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Countably compact space
In mathematics a topological space is countably compact if every countable open cover has a finite subcover.
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Cover (topology)
In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset.
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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
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Cut-the-Knot
Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.
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Dense set
In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
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Diagram (category theory)
In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory.
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Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
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Discrete space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.
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Domain theory
Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains.
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Edit distance
In computational linguistics and computer science, edit distance is a way of quantifying how dissimilar two strings (e.g., words) are to one another by counting the minimum number of operations required to transform one string into the other.
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Eduard Heine
Heinrich Eduard Heine (16 March 1821, Berlin – October 1881, Halle) was a German mathematician.
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Element (mathematics)
In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.
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Elliptic geometry
Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.
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Enriched category
In category theory, a branch of mathematics, an enriched category generalizes the idea of a category by replacing hom-sets with objects from a general monoidal category.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Euclidean distance
In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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European Mathematical Society
The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe.
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Extended real number line
In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).
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Felix Hausdorff
Felix Hausdorff (November 8, 1868 – January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Finite set
In mathematics, a finite set is a set that has a finite number of elements.
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First-countable space
In topology, a branch of mathematics, a first-countable space is a topological space satisfying the "first axiom of countability".
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function space
In mathematics, a function space is a set of functions between two fixed sets.
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Game theory
Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".
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Geometric group theory
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).
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Glossary of Riemannian and metric geometry
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph edit distance
In mathematics and computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs.
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Graph operations
Graph operations produce new graphs from initial ones.
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Gromov–Hausdorff convergence
In mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence.
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Hausdorff distance
In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other.
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Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
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Heine–Borel theorem
In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S of Euclidean space Rn, the following two statements are equivalent.
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Heine–Cantor theorem
In mathematics, the Heine–Cantor theorem, named after Eduard Heine and Georg Cantor, states that if f: M → N is a continuous function between two metric spaces, and M is compact, then f is uniformly continuous.
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Helly metric
In game theory, the Helly metric is used to assess the distance between two strategies.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Hilbert's fourth problem
In mathematics, Hilbert's fourth problem in the 1900 Hilbert problems is a foundational question in geometry.
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Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
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Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.
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Hyperboloid model
In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model (after Hermann Minkowski and Hendrik Lorentz), is a model of n-dimensional hyperbolic geometry in which points are represented by the points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space and m-planes are represented by the intersections of the (m+1)-planes in Minkowski space with S+.
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Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
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Identity of indiscernibles
The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Image (mathematics)
In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.
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Infimum and supremum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
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King (chess)
In chess, the king (♔,♚) is the most important piece.
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Kuratowski convergence
In mathematics, Kuratowski convergence is a notion of convergence for sequences (or, more generally, nets) of compact subsets of metric spaces, named after Kazimierz Kuratowski.
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Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
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Lebesgue's number lemma
In topology, Lebesgue's number lemma, named after Henri Lebesgue, is a useful tool in the study of compact metric spaces.
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Levenshtein distance
In information theory, linguistics and computer science, the Levenshtein distance is a string metric for measuring the difference between two sequences.
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Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
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Lindelöf space
In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover.
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Line (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
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Line segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
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Lipschitz continuity
In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.
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Locally compact space
In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.
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Locally connected space
In topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting entirely of open, connected sets.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Maurice René Fréchet
Maurice Fréchet (2 September 1878 – 4 June 1973) was a French mathematician.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Metric (mathematics)
In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.
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Metric map
In the mathematical theory of metric spaces, a metric map is a function between metric spaces that does not increase any distance (such functions are always continuous).
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Metric signature
The signature of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive and zero eigenvalues of the real symmetric matrix of the metric tensor with respect to a basis.
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Metric tensor
In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.
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Metric tree
A metric tree is any tree data structure specialized to index data in metric spaces.
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Metrization theorem
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.
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Monoidal category
In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor that is associative up to a natural isomorphism, and an object I that is both a left and right identity for ⊗, again up to a natural isomorphism.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Nati Linial
Nathan (Nati) Linial (born 1953 in Haifa, Israel) is an Israeli mathematician and computer scientist, a professor in the Rachel and Selim Benin School of Computer Science and Engineering at the Hebrew University of Jerusalem, and an ISI highly cited researcher.
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Normal space
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods.
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Normed vector space
In mathematics, a normed vector space is a vector space over the real or complex numbers, on which a norm is defined.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Ordered pair
In mathematics, an ordered pair (a, b) is a pair of objects.
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Paracompact space
In mathematics, a paracompact space is a topological space in which every open cover has an open refinement that is locally finite.
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Partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.
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Partition of unity
In mathematics, a partition of unity of a topological space X is a set R of continuous functions from X to the unit interval such that for every point, x\in X,.
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Pavel Alexandrov
Pavel Sergeyevich Alexandrov (Па́вел Серге́евич Алекса́ндров), sometimes romanized Paul Alexandroff or Aleksandrov (7 May 1896 – 16 November 1982), was a Soviet mathematician.
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Pavel Urysohn
Pavel Samuilovich Urysohn (Па́вел Самуи́лович Урысо́н) (February 3, 1898 – August 17, 1924) was a Soviet mathematician of Jewish origin who is best known for his contributions in dimension theory, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology.
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Positive real numbers
In mathematics, the set of positive real numbers, \mathbb_.
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Product metric
In mathematics, a product metric is a metric on the Cartesian product of finitely many metric spaces (X_1,d_),\ldots,(X_n,d_) which metrizes the product topology.
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Product topology
In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology.
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Pseudometric space
In mathematics, a pseudometric space is a generalized metric space in which the distance between two distinct points can be zero.
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Quasi-isometry
In mathematics, quasi-isometry is an equivalence relation on metric spaces that ignores their small-scale details in favor of their coarse structure.
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Rank (linear algebra)
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
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Second-countable space
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.
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Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Sequential space
In topology and related fields of mathematics, a sequential space is a topological space that satisfies a very weak axiom of countability.
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Sequentially compact space
In mathematics, a topological space is sequentially compact if every infinite sequence has a convergent subsequence.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Sign (mathematics)
In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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SNCF
The Société nationale des chemins de fer français (SNCF, "French National Railway Company") is France's national state-owned railway company.
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Space (mathematics)
In mathematics, a space is a set (sometimes called a universe) with some added structure.
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Special relativity
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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String (computer science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.
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Subadditivity
In mathematics, subadditivity is a property of a function that states, roughly, that evaluating the function for the sum of two elements of the domain always returns something less than or equal to the sum of the function's values at each element.
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Subsequence
In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.
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Subset
In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.
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Surjective function
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
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Symmetric function
In mathematics, a symmetric function of n variables is one whose value given n arguments is the same no matter the order of the arguments.
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T-theory
T-theory is a branch of discrete mathematics dealing with analysis of trees and discrete metric spaces.
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Taxicab geometry
A taxicab geometry is a form of geometry in which the usual distance function or metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the absolute differences of their Cartesian coordinates.
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Tensor product
In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.
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Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
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Tietze extension theorem
In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary.
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Tight span
In metric geometry, the metric envelope or tight span of a metric space M is an injective metric space into which M can be embedded.
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Topological property
In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Totally bounded space
In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of every fixed "size" (where the meaning of "size" depends on the given context).
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Triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
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Tychonoff space
In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces.
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Ultrametric space
In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d(x,z)\leq\max\left\.
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Uniform continuity
In mathematics, a function f is uniformly continuous if, roughly speaking, it is possible to guarantee that f(x) and f(y) be as close to each other as we please by requiring only that x and y are sufficiently close to each other; unlike ordinary continuity, the maximum distance between f(x) and f(y) cannot depend on x and y themselves.
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Uniform isomorphism
In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties.
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Uniform norm
In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions f defined on a set S the non-negative number This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. The name "uniform norm" derives from the fact that a sequence of functions \ converges to f under the metric derived from the uniform norm if and only if f_n converges to f uniformly.
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Uniform space
In the mathematical field of topology, a uniform space is a set with a uniform structure.
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Universal property
In various branches of mathematics, a useful construction is often viewed as the “most efficient solution” to a certain problem.
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Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
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Word metric
In group theory, a branch of mathematics, a word metric on a group G is a way to measure distance between any two elements of G. As the name suggests, the word metric is a metric on G, assigning to any two elements g, h of G a distance d(g,h) that measures how efficiently their difference g^ h can be expressed as a word whose letters come from a generating set for the group.
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Yuri Burago
Yuri Dmitrievich Burago (Ю́рий Дми́триевич Бура́го) (born 1936) is a Russian mathematician.
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(ε, δ)-definition of limit
In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit.
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Bounded metric, Bounded metric space, Bounded space, British rail metric, Compact metric space, Discrete metric space, Distance to a set, Finite metric space, Metric Geometry, Metric geometry, Metric spaces, Metric topology, Post Office metric, Post office metric, Postoffice metric, Quotient metric space, Reimann space, Riemann space, SNCF metric.
References
[1] https://en.wikipedia.org/wiki/Metric_space
