# Hausdorff space

$T_2$-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://www.encyclopediaofmath.org/index.php?title=Hausdorff_space&oldid=31028
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