In topology and related branches of mathematics, a **Hausdorff space**, **separated space** or **T _{2} space** is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T

_{2}) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters.

Hausdorff spaces are named for 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.

Read more about Hausdorff Space: Definitions, Equivalences, Examples and Counterexamples, Properties, Preregularity Versus Regularity, Variants, Algebra of Functions, Academic Humour

### Other articles related to "hausdorff space, space, hausdorff, spaces, hausdorff spaces":

**Hausdorff Space**- Relation To Other Separation Axioms

... It follows that every completely

**Hausdorff space**is Urysohn and every Urysohn

**space**is

**Hausdorff**... One can also show that every regular

**Hausdorff space**is Urysohn and every Tychonoff

**space**(=completely regular

**Hausdorff space**) is completely

**Hausdorff**...

... of closed set is defined above in terms of open sets, a concept that makes sense for topological

**spaces**, as well as for other

**spaces**that carry topological structures, such ... A subset A of a topological

**space**X is closed in X if and only if every limit of every net of elements of A also belongs to A ... In a first-countable

**space**(such as a metric

**space**), it is enough to consider only convergent sequences, instead of all nets ...

... Every continuous image of a compact

**space**is compact ... Tychonoff's theorem the (arbitrary) product of compact

**spaces**is compact ... A compact subset of a

**Hausdorff space**is closed ...

**Hausdorff Space**

... In mathematics, a weak

**Hausdorff space**or weakly

**Hausdorff space**is a topological

**space**where the image of every continuous map from a compact

**Hausdorff space**... In particular, every

**Hausdorff space**is weak

**Hausdorff**... of working with the category of

**Hausdorff spaces**...

**Hausdorff Space**- Academic Humour

...

**Hausdorff**condition is illustrated by the pun that in

**Hausdorff spaces**any two points can be "housed off" from each other by open sets ... In the Mathematics Institute of at the University of Bonn, in which Felix

**Hausdorff**researched and lectured, there is a certain room designated the

**Hausdorff**-Raum (Raum stands for both

**space**...

### Famous quotes containing the word space:

“In the United States there is more *space* where nobody is is than where anybody is.”

—Gertrude Stein (1874–1946)