Compact space, countably

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.

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