Back فضاء هاوسدورف Arabic Хаусдорфово пространство Bulgarian Espai de Hausdorff Catalan Hausdorffův prostor Czech Хаусдорф уçлăхĕ CV Hausdorffrum Danish Hausdorff-Raum German Hausdorff-a spaco Esperanto Espacio de Hausdorff Spanish Hausdorffi ruum Estonian
| Separation axioms in topological spaces | |
|---|---|
| Kolmogorov classification | |
| T0 | (Kolmogorov) |
| T1 | (Fréchet) |
| T2 | (Hausdorff) |
| T2½ | (Urysohn) |
| completely T2 | (completely Hausdorff) |
| T3 | (regular Hausdorff) |
| T3½ | (Tychonoff) |
| T4 | (normal Hausdorff) |
| T5 | (completely normal Hausdorff) |
| T6 | (perfectly normal Hausdorff) |
In topology and related branches of mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf[1]), separated space or T2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each that are disjoint from each other. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters.[2]
Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology. Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an axiom.
- ^ "Hausdorff space Definition & Meaning". www.dictionary.com. Retrieved 15 June 2022.
- ^ "Separation axioms in nLab". ncatlab.org.