Difference between revisions of "Dominant of a topological space"
From Encyclopedia of Mathematics
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| − | Any topological space for which | + | Any topological space for which $X$ serves as a retract (cf. [[Retract of a topological space]]). |
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| − | This is not standard Western terminology; there is in fact no name for this concept. The standard Western usage of dominating is as follows: A space | + | This is not standard Western terminology; there is in fact no name for this concept. The standard Western usage of dominating is as follows: A space $X$ is said to dominate a space $Y$ if and only if there are continuous mappings $f : X \rightarrow Y$ and $g : Y \rightarrow X$ such that $fg$ is homotopic to the identity mapping (on $Y$). |
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Latest revision as of 17:20, 29 September 2016
$X$
Any topological space for which $X$ serves as a retract (cf. Retract of a topological space).
Comments
This is not standard Western terminology; there is in fact no name for this concept. The standard Western usage of dominating is as follows: A space $X$ is said to dominate a space $Y$ if and only if there are continuous mappings $f : X \rightarrow Y$ and $g : Y \rightarrow X$ such that $fg$ is homotopic to the identity mapping (on $Y$).
How to Cite This Entry:
Dominant of a topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dominant_of_a_topological_space&oldid=39348
Dominant of a topological space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dominant_of_a_topological_space&oldid=39348
This article was adapted from an original article by A.V. Chernavskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article