# Extension of a topological space

From Encyclopedia of Mathematics

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

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

#### References

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

**How to Cite This Entry:**

Extension of a topological space.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Extension_of_a_topological_space&oldid=34339

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