# Difference between revisions of "Hausdorff space"

From Encyclopedia of Mathematics

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+ | $T_2$-''space'' | ||

− | A topological space in which any two (distinct) points are separated by disjoint | + | A [[topological space]] in which any two (distinct) points are separated by disjoint [[neighbourhood]]s (see [[Hausdorff axiom]]). Hausdorff spaces need not be [[regular space]]s nor a fortiori [[completely-regular space]]s, 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 [[#References|[1]]]. |

====References==== | ====References==== | ||

− | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> F. Hausdorff, "Set theory" , Chelsea, reprint (1978) (Translated from German)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)</TD></TR></table> | + | <table> |

+ | <TR><TD valign="top">[1]</TD> <TD valign="top"> F. Hausdorff, "Set theory" , Chelsea, reprint (1978) (Translated from German)</TD></TR> | ||

+ | <TR><TD valign="top">[2]</TD> <TD valign="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)</TD></TR> | ||

+ | </table> | ||

+ | |||

+ | [[Category:General topology]] |

## Latest revision as of 22:21, 7 November 2014

$T_2$-*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=18077

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