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...

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

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...

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,...

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...

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...

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...