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...

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

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...

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

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...

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

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...

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...

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

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...

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

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

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...

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

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...

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...

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

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

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

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 in Wiktionary, the free dictionary. Hausdorff may refer to: A Hausdorff space, when used as an adjective, as in "the real line is Hausdorff"...

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...

disconnected compact Hausdorff space. Every Stonean space is a Stone space, but not vice versa. In the duality between Stone spaces and Boolean algebras...

Felix Hausdorff (/ˈhaʊsdɔːrf/ HOWS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré...