Difference between revisions of "Compactness"
From Encyclopedia of Mathematics
(Importing text file) |
(Added TeX done tag; rewrite for clarity.) |
||
| Line 1: | Line 1: | ||
| − | A property which characterizes a wide class of topological spaces, requiring that from any covering of a space by open sets it is possible to extract a finite covering | + | {{TEX|done}} |
| − | + | A property which characterizes a wide class of topological spaces, requiring that from any covering of a space by open sets it is possible to extract a finite covering. Topological spaces with the compactness property are called [[Compact space|compact spaces. In Russian literature, "compactness" is often used for the notion of countable compactness, and "bicompactness" for general compactness. | |
| − | |||
| − | |||
| − | |||
| − | " | ||
For references, see [[Compact space|Compact space]]. | For references, see [[Compact space|Compact space]]. | ||
Revision as of 06:35, 23 April 2012
A property which characterizes a wide class of topological spaces, requiring that from any covering of a space by open sets it is possible to extract a finite covering. Topological spaces with the compactness property are called [[Compact space|compact spaces. In Russian literature, "compactness" is often used for the notion of countable compactness, and "bicompactness" for general compactness.
For references, see Compact space.
How to Cite This Entry:
Compactness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compactness&oldid=11573
Compactness. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compactness&oldid=11573
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