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24 relations: Boundary (topology), Closed set, Closure (topology), Compact space, Euclidean space, Georg Nöbeling, Hausdorff space, Irrational number, Ivor Grattan-Guinness, Karl Menger, Lebesgue covering dimension, Mathematical induction, Metric space, Metrization theorem, Miroslav Katětov, Normal space, Open set, Pavel Alexandrov, Second-countable space, Separable space, Sphere, Subset, Topological space, Topology.
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.
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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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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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Georg Nöbeling
Georg August Nöbeling (12 November 1907 – 16 February 2008) was a German mathematician.
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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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Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
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Ivor Grattan-Guinness
Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic.
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Karl Menger
Karl Menger (January 13, 1902 – October 5, 1985) was an Austrian-American mathematician.
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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.
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Mathematical induction
Mathematical induction is a mathematical proof technique.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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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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Miroslav Katětov
Miroslav Katětov (March 17, 1918, Chembar, Russia – December 15, 1995) was a Czech mathematician, chess master, and psychologist.
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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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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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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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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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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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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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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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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.
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Large inductive dimension, Menger-Urysohn dimension, Menger–Urysohn dimension, Nobeling space, Nobeling-Pontryagin theorem, Nobeling–Pontryagin theorem, Noebeling space, Noebeling-Pontryagin theorem, Nöbeling space, Nöbeling-Pontryagin theorem, Nöbeling–Pontryagin theorem, Small inductive dimension.
References
[1] https://en.wikipedia.org/wiki/Inductive_dimension
