mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), T2 space or separated space, is a topological space where distinct points...
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normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space...
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a topological space in which every point has a compact neighborhood. In mathematical analysis locally compact spaces that are Hausdorff are of particular...
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compact space into a Hausdorff space is a homeomorphism. A compact Hausdorff space is normal and regular. If a space X is compact and Hausdorff, then no...
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Dieudonné (1944). Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it...
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neighborhoods. A T3 space or regular Hausdorff space is a topological space that is both regular and a Hausdorff space. (A Hausdorff space or T2 space is a topological...
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space, or T2½ space, is a topological space in which any two distinct points can be separated by closed neighborhoods. A completely Hausdorff space,...
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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...
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completely regular space that is also a Hausdorff space; there exist completely regular spaces that are not Tychonoff (i.e. not Hausdorff). Paul Urysohn had...
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a Hausdorff space (although this article does not). One of the most widely studied categories of TVSs are locally convex topological vector spaces. This...
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particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense...
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Also some authors include some separation axiom (like Hausdorff space or weak Hausdorff space) in the definition of one or both terms, and others don't...
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above agree for separable, metrisable spaces.[citation needed][clarification needed] A zero-dimensional Hausdorff space is necessarily totally disconnected...
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For example, the line with two origins is not a Hausdorff space but is locally Hausdorff. Sierpiński space is a simple example of a topology that is T0 but...
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mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization...
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space is automatically assumed to carry this Hausdorff topology, unless indicated otherwise. With this topology, every Banach space is a Baire space,...
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with metric spaces, every uniform space X {\displaystyle X} has a Hausdorff completion: that is, there exists a complete Hausdorff uniform space Y {\displaystyle...
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surface is a topological space that is locally like a Euclidean plane. Topological spaces were first defined by Felix Hausdorff in 1914 in his seminal "Principles...
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Arzelà–Ascoli theorem (category Topology of function spaces)
compact metric space (Dunford & Schwartz 1958, p. 382). Modern formulations of the theorem allow for the domain to be compact Hausdorff and for the range...
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space to be metrizable. Metrizable spaces inherit all topological properties from metric spaces. For example, they are Hausdorff paracompact spaces (and...
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space is said to be locally Hausdorff if every point has a neighbourhood that is a Hausdorff space under the subspace topology. Every Hausdorff space...
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onto the unit square (any continuous bijection from a compact space onto a Hausdorff space is a homeomorphism). But a unit square has no cut-point, and...
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to as the Hausdorff–Besicovitch dimension. More specifically, the Hausdorff dimension is a dimensional number associated with a metric space, i.e. a set...
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totally disconnected Hausdorff space that does not have small inductive dimension 0. Extremally disconnected Hausdorff spaces Stone spaces The Knaster–Kuratowski...
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mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each...
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Every R1 space is also R0. X is Hausdorff, or T2 or separated, if any two distinct points in X are separated by neighbourhoods. Thus, X is Hausdorff if and...
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Hausdorff in Wiktionary, the free dictionary. Hausdorff may refer to: A Hausdorff space, when used as an adjective, as in "the real line is Hausdorff"...
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strings of characters, or the Gromov–Hausdorff distance between metric spaces themselves). Formally, a metric space is an ordered pair (M, d) where M is...
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disconnected compact Hausdorff space. Every Stonean space is a Stone space, but not vice versa. In the duality between Stone spaces and Boolean algebras...
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Felix Hausdorff (/ˈhaʊsdɔːrf/ HOWS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré...
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