Hausdorff space information

mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), separated space or T2 space is a topological space where, for any two...

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...

Dieudonné (1944). Every compact space is paracompact. Every paracompact Hausdorff space is normal, and a Hausdorff space is paracompact if and only if it...

a topological space in which every point has a compact neighborhood. In mathematical analysis locally compact spaces that are Hausdorff are of particular...

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...

space, or T2½ space, is a topological space in which any two distinct points can be separated by closed neighborhoods. A completely Hausdorff space,...

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...

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...

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...

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...

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...

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...

a Hausdorff space (although this article does not). One of the most widely studied categories of TVSs are locally convex topological vector spaces. This...

space to be metrizable. Metrizable spaces inherit all topological properties from metric spaces. For example, they are Hausdorff paracompact spaces (and...

with metric spaces, every uniform space X {\displaystyle X} has a Hausdorff completion: that is, there exists a complete Hausdorff uniform space Y {\displaystyle...

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...

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...

space is automatically assumed to carry this Hausdorff topology, unless indicated otherwise. With this topology, every Banach space is a Baire space,...

totally disconnected Hausdorff space that does not have small inductive dimension 0. Extremally disconnected Hausdorff spaces Stone spaces The Knaster–Kuratowski...

to as the Hausdorff–Besicovitch dimension. More specifically, the Hausdorff dimension is a dimensional number associated with a metric space, i.e. a set...

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"...

Completely normal Hausdorff A completely normal Hausdorff space (or T5 space) is a completely normal T1 space. (A completely normal space is Hausdorff if and only...

mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each...

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...

first introduced). After the notion of a general topological space was defined by Felix Hausdorff in 1914, although locally convex topologies were implicitly...