Hausdorff space
Sign in to saveAlso known as separated space, T₂ space, T2 space
topological space in which distinct points have disjoint neighbourhoods
Key facts
- T 0
- (Kolmogorov)
- T 1
- (Fréchet)
- T 2
- (Hausdorff)
- Completely t 2
- (completely Hausdorff)
- T 3
- (regular Hausdorff)
- T 4
- (normal Hausdorff)
- T 5
- (completely normal, Hausdorff)
- T 6
- (perfectly normal, Hausdorff)
via Wikipedia infobox
Wikidata facts
- Named after
- Felix Hausdorff
- Image
- Hausdorff space.svg
Show 3 more facts
- Stack Exchange tag
- mathoverflow.net/tags/hausdorff-spaces
- maintained by WikiProject
- WikiProject Mathematics
- has characteristic
- separation axiom
Sources (3)
via Wikidata · CC0
~13 min read
Encyclopedic overview
In topology and related branches of mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), T2 space or separated space, is a topological space where distinct points have disjoint neighbourhoods. 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.
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.
Excerpted from Wikipedia’s “Hausdorff space” article, available under the CC BY-SA 4.0 licence.