Difference between revisions of "Extension of a topological space"
From Encyclopedia of Mathematics
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| + | A topological space $Y$ in which the given topological space $X$ is an everywhere-dense subspace. If $Y$ is compact, then it is called a compact extension, and if $Y$ is Hausdorff, it is called a Hausdorff extension. | ||
Revision as of 19:16, 7 July 2014
A topological space $Y$ in which the given topological space $X$ is an everywhere-dense subspace. If $Y$ is compact, then it is called a compact extension, and if $Y$ is Hausdorff, 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=13372
Extension of a topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Extension_of_a_topological_space&oldid=13372
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article