## Hausdorff Space

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.

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### Some articles on hausdorff space:

**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**... we have the following implications Tychonoff (T3½) regular

**Hausdorff**(T3) completely

**Hausdorff**Urysohn (T2½)

**Hausdorff**(T2) T1 One can find counterexamples showing that none of these ...

**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**and room in German) ...

**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**into the

**space**is closed ... In particular, every

**Hausdorff space**is weak

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

**Hausdorff spaces**...

... 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 as metric

**spaces**, differentiable ... 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 ...

### Famous quotes containing the word space:

“To play is nothing but the imitative substitution of a pleasurable, superfluous and voluntary action for a serious, necessary, imperative and difficult one. At the cradle of play as well as of artistic activity there stood leisure, tedium entailed by increased spiritual mobility, a horror vacui, the need of letting forms no longer imprisoned move freely, of filling empty time with sequences of notes, empty *space* with sequences of form.”

—Max J. Friedländer (1867–1958)