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Difference between revisions of "Semi-continuous decomposition"

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A [[Decomposition|decomposition]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084000/s0840001.png" />, i.e. a closed disjoint covering, of a topological space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084000/s0840002.png" /> such that the [[Quotient mapping|quotient mapping]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084000/s0840003.png" /> is closed (open) (cf. [[Open mapping|Open mapping]]; [[Closed mapping|Closed mapping]]).
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A [[decomposition]] $D$, i.e. a closed disjoint covering, of a topological space $X$ such that the [[quotient mapping]] $p : X \rightarrow D$ is a [[closed mapping]] ([[open mapping]]).
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Latest revision as of 20:20, 9 December 2016

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A decomposition $D$, i.e. a closed disjoint covering, of a topological space $X$ such that the quotient mapping $p : X \rightarrow D$ is a closed mapping (open mapping).

How to Cite This Entry:
Semi-continuous decomposition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-continuous_decomposition&oldid=17298
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article