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 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 (cf. [[Second axiom of countability]]). 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> | ||
Revision as of 16:12, 29 September 2013
$T_2$-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 (cf. Second axiom of countability). 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=30575
Hausdorff space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hausdorff_space&oldid=30575
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