Difference between revisions of "Compact space, countably"
From Encyclopedia of Mathematics
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| − | A topological space possessing the property of countable compactness (cf. [[Compactness, countable|Compactness, countable]]). A metrizable (countably) compact space is called a [[Compactum|compactum]]. Sometimes the term "countably compact space" means a countably [[Compact space|compact space]] which satisfies an additional separation property; a space without the latter property is then called quasi countably compact. A space that can be represented as a countable union of countably compact spaces is called | + | {{TEX|done}} |
| + | A topological space possessing the property of countable compactness (cf. [[Compactness, countable|Compactness, countable]]). A metrizable (countably) compact space is called a [[Compactum|compactum]]. Sometimes the term "countably compact space" means a countably [[Compact space|compact space]] which satisfies an additional separation property; a space without the latter property is then called quasi countably compact. A space that can be represented as a countable union of countably compact spaces is called $\sigma$-countably compact. | ||
Latest revision as of 16:43, 30 July 2014
A topological space possessing the property of countable compactness (cf. Compactness, countable). A metrizable (countably) compact space is called a compactum. Sometimes the term "countably compact space" means a countably compact space which satisfies an additional separation property; a space without the latter property is then called quasi countably compact. A space that can be represented as a countable union of countably compact spaces is called $\sigma$-countably compact.
Comments
The additional separation condition referred to in the article above is the Hausdorff property.
How to Cite This Entry:
Compact space, countably. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compact_space,_countably&oldid=32585
Compact space, countably. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Compact_space,_countably&oldid=32585
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article