Faster access than browser!
63 relations: Allen Hatcher, Archiv der Mathematik, Banach manifold, Boundary (topology), Cambridge University Press, Cantor set, Closed set, Codomain, Cofibration, Compact space, Compact-open topology, Compactly generated space, Complete metric space, Connected space, Continuous function, Contractible space, Convex set, Cover (topology), CW complex, Elsevier, F-space, Fundamenta Mathematicae, Hausdorff space, Hilbert cube, Hilbert manifold, Homeomorphism, Homotopy, Homotopy extension property, Homotopy group, Idempotence, Identity function, If and only if, Inclusion map, J. H. C. Whitehead, James Dugundji, John Milnor, Karol Borsuk, Lebesgue covering dimension, Local property, Locally compact space, Locally connected space, Loop space, Metrization theorem, N-sphere, Normal space, Normed vector space, North Holland, Olof Hanner, Pathological (mathematics), Separable space, ..., Subspace topology, Surjective function, Topological manifold, Topological pair, Topological space, Topological vector space, Topology, Transactions of the American Mathematical Society, Unit cube, University of Chicago Press, Weak Hausdorff space, Whitehead theorem, Witold Hurewicz. Expand index (13 more) »
Allen Hatcher
Allen Edward Hatcher (born October 23, 1944) is an American topologist.
New!!: Retract and Allen Hatcher · See more »
Archiv der Mathematik
Archiv der Mathematik is a peer-reviewed mathematics journal published by Springer, established in 1948.
New!!: Retract and Archiv der Mathematik · See more »
Banach manifold
In mathematics, a Banach manifold is a manifold modeled on Banach spaces.
New!!: Retract and Banach manifold · See more »
Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.
New!!: Retract and Boundary (topology) · See more »
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
New!!: Retract and Cambridge University Press · See more »
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.
New!!: Retract and Cantor set · See more »
Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
New!!: Retract and Closed set · See more »
Codomain
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
New!!: Retract and Codomain · See more »
Cofibration
In mathematics, in particular homotopy theory, a continuous mapping where A and X are topological spaces, is a cofibration if it satisfies the homotopy extension property with respect to all spaces Y. This definition is dual to that of a fibration, which is required to satisfy the homotopy lifting property with respect to all spaces.
New!!: Retract and Cofibration · See more »
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).
New!!: Retract and Compact space · See more »
Compact-open topology
In mathematics, the compact-open topology is a topology defined on the set of continuous maps between two topological spaces.
New!!: Retract and Compact-open topology · See more »
Compactly generated space
In topology, a compactly generated space (or k-space) is a topological space whose topology is coherent with the family of all compact subspaces.
New!!: Retract and Compactly generated space · See more »
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).
New!!: Retract and Complete metric space · See more »
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.
New!!: Retract and Connected space · See more »
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.
New!!: Retract and Continuous function · See more »
Contractible space
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.
New!!: Retract and Contractible space · See more »
Convex set
In convex geometry, a convex set is a subset of an affine space that is closed under convex combinations.
New!!: Retract and Convex set · See more »
Cover (topology)
In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset.
New!!: Retract and Cover (topology) · See more »
CW complex
In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory.
New!!: Retract and CW complex · See more »
Elsevier
Elsevier is an information and analytics company and one of the world's major providers of scientific, technical, and medical information.
New!!: Retract and Elsevier · See more »
F-space
In functional analysis, an F-space is a vector space V over the real or complex numbers together with a metric d: V × V → R so that.
New!!: Retract and F-space · See more »
Fundamenta Mathematicae
Fundamenta Mathematicae is a peer-reviewed scientific journal of mathematics with a special focus on the foundations of mathematics, concentrating on set theory, mathematical logic, topology and its interactions with algebra, and dynamical systems.
New!!: Retract and Fundamenta Mathematicae · See more »
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.
New!!: Retract and Hausdorff space · See more »
Hilbert cube
In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology.
New!!: Retract and Hilbert cube · See more »
Hilbert manifold
In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces.
New!!: Retract and Hilbert manifold · See more »
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.
New!!: Retract and Homeomorphism · See more »
Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
New!!: Retract and Homotopy · See more »
Homotopy extension property
In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space.
New!!: Retract and Homotopy extension property · See more »
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces.
New!!: Retract and Homotopy group · See more »
Idempotence
Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application.
New!!: Retract and Idempotence · See more »
Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
New!!: Retract and Identity function · See more »
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.
New!!: Retract and If and only if · See more »
Inclusion map
In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element, x, of A to x, treated as an element of B: A "hooked arrow" is sometimes used in place of the function arrow above to denote an inclusion map; thus: \iota: A\hookrightarrow B. (On the other hand, this notation is sometimes reserved for embeddings.) This and other analogous injective functions from substructures are sometimes called natural injections.
New!!: Retract and Inclusion map · See more »
J. H. C. Whitehead
John Henry Constantine Whitehead FRS (11 November 1904 – 8 May 1960), known as Henry, was a British mathematician and was one of the founders of homotopy theory.
New!!: Retract and J. H. C. Whitehead · See more »
James Dugundji
James Dugundji (August 30, 1919 – January, 1985) was an American mathematician, a professor of mathematics at the University of Southern California.
New!!: Retract and James Dugundji · See more »
John Milnor
John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, K-theory and dynamical systems.
New!!: Retract and John Milnor · See more »
Karol Borsuk
Karol Borsuk (May 8, 1905 – January 24, 1982) was a Polish mathematician.
New!!: Retract and Karol Borsuk · See more »
Lebesgue covering dimension
In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.
New!!: Retract and Lebesgue covering dimension · See more »
Local property
In mathematics, a phenomenon is sometimes said to occur locally if, roughly speaking, it occurs on sufficiently small or arbitrarily small neighborhoods of points.
New!!: Retract and Local property · See more »
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.
New!!: Retract and Locally compact space · See more »
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.
New!!: Retract and Locally connected space · See more »
Loop space
In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X, maps from the circle S1 to X, equipped with the compact-open topology.
New!!: Retract and Loop space · See more »
Metrization theorem
In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space.
New!!: Retract and Metrization theorem · See more »
N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
New!!: Retract and N-sphere · See more »
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.
New!!: Retract and Normal space · See more »
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.
New!!: Retract and Normed vector space · See more »
North Holland
North Holland (Noord-Holland, West Frisian Dutch: Noard-Holland) is a province of the Netherlands located in the northwestern part of the country.
New!!: Retract and North Holland · See more »
Olof Hanner
Olof Hanner (7 December 1922 in Stockholm – 19 September 2015 in Gothenburg) was a Swedish mathematician.
New!!: Retract and Olof Hanner · See more »
Pathological (mathematics)
In mathematics, a pathological phenomenon is one whose properties are considered atypically bad or counterintuitive; the opposite is well-behaved.
New!!: Retract and Pathological (mathematics) · See more »
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.
New!!: Retract and Separable space · See more »
Subspace topology
In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).
New!!: Retract and Subspace topology · See more »
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).
New!!: Retract and Surjective function · See more »
Topological manifold
In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below.
New!!: Retract and Topological manifold · See more »
Topological pair
In mathematics, more specifically algebraic topology, a pair (X,A) is shorthand for an inclusion of topological spaces i\colon A\hookrightarrow X. Sometimes i is assumed to be a cofibration.
New!!: Retract and Topological pair · See more »
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.
New!!: Retract and Topological space · See more »
Topological vector space
In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.
New!!: Retract and Topological vector space · See more »
Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
New!!: Retract and Topology · See more »
Transactions of the American Mathematical Society
The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.
New!!: Retract and Transactions of the American Mathematical Society · See more »
Unit cube
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.
New!!: Retract and Unit cube · See more »
University of Chicago Press
The University of Chicago Press is the largest and one of the oldest university presses in the United States.
New!!: Retract and University of Chicago Press · See more »
Weak Hausdorff space
In mathematics, a weak Hausdorff space or weakly Hausdorff space is a topological space where the image of every continuous map from a compact Hausdorff space into the space is closed.
New!!: Retract and Weak Hausdorff space · See more »
Whitehead theorem
In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence.
New!!: Retract and Whitehead theorem · See more »
Witold Hurewicz
Witold Hurewicz (June 29, 1904 – September 6, 1956) was a Jewish-Polish mathematician.
New!!: Retract and Witold Hurewicz · See more »
Redirects here:
Absolute neighborhood retract, Absolute retract, Defamation retraction, Deformation retract, Deformation retraction, NDR-pair, Neighborhood deformation retract, Neighborhood retract, No-retraction theorem, Strong deformation retract.
References
[1] https://en.wikipedia.org/wiki/Retract
