Difference between revisions of "Extension of a topological space"
From Encyclopedia of Mathematics
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| − | A topological space | + | {{TEX|done}} |
| + | 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==== | ====Comments==== | ||
| − | Compact extensions are also called compactifications, cf. also [[ | + | Compact extensions are also called compactifications, cf. also [[Compactification]]. |
====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Čech, "Topological spaces" , Wiley (1966)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Čech, "Topological spaces" , Wiley (1966)</TD></TR></table> | ||
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| + | [[Category:General topology]] | ||
Latest revision as of 22:21, 7 November 2014
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=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