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
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article