Extension of a topological space

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A topological space $Y$ in which the given topological space $X$ is an everywhere-dense set. If $Y$ is a compact space, then it is called a compact extension, and if $Y$ is a Hausdorff space, it is called a Hausdorff extension.


Compact extensions are also called compactifications, cf. also Compactification.


[a1] E. Čech, "Topological spaces" , Wiley (1966)
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Extension of a topological space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article