# Hausdorff space

From Encyclopedia of Mathematics

$T_2$-*space*

A topological space in which any two (distinct) points are separated by disjoint neighbourhoods (see Hausdorff axiom). Hausdorff spaces need not be regular spaces nor a fortiori completely-regular spaces, even when they consist only of a countable set of points or have a countable base. They were first considered by F. Hausdorff in 1914, see [1].

#### References

[1] | F. Hausdorff, "Set theory" , Chelsea, reprint (1978) (Translated from German) |

[2] | A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian) |

**How to Cite This Entry:**

Hausdorff space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Hausdorff_space&oldid=34338

This article was adapted from an original article by A.V. Arkhangel'skii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article