Extension of a topological space

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.

#### Comments[edit]

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

#### References[edit]

[a1] |  E. Čech, "Topological spaces" , Wiley (1966)

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