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

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...

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...

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

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...

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

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

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...

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...

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...

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...

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...

mathematics, Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization...

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

above agree for separable, metrisable spaces.[citation needed][clarification needed] A zero-dimensional Hausdorff space is necessarily totally disconnected...

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

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...

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

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...

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

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...

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

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...

Hausdorff or locally connected. A space in which all components are one-point sets is called totally disconnected. Related to this property, a space X...

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...

space X to a compact Hausdorff space βX. The Stone–Čech compactification βX of a topological space X is the largest, most general compact Hausdorff space...

Hausdorff in Wiktionary, the free dictionary. Hausdorff may refer to: Felix Hausdorff (1868–1942), German mathematician after whom Hausdorff spaces are...