View source for Compact space, countably

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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 $\sigma$-countably compact.



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The additional separation condition referred to in the article above is the Hausdorff property.