Difference between revisions of "Hausdorff space"
From Encyclopedia of Mathematics
(Importing text file) |
m (links) |
||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | '' | + | {{TEX|done}} |
| + | $T_2$-''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
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