Namespaces
Variants
Actions

Difference between revisions of "Extension of a topological space"

From Encyclopedia of Mathematics
Jump to: navigation, search
(TeX)
m (links)
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
 
{{TEX|done}}
 
{{TEX|done}}
−
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.
+
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 [[Compactification|Compactification]].
+
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>
 +
 +
[[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=32390
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
Retrieved from "https://encyclopediaofmath.org/index.php?title=Extension_of_a_topological_space&oldid=34339"