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Difference between revisions of "Continuous section"

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A continuous mapping <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025740/c0257401.png" /> of the image <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025740/c0257402.png" /> of a continuous mapping <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025740/c0257403.png" /> of topological spaces <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025740/c0257404.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025740/c0257405.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025740/c0257406.png" /> is the identity mapping on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025740/c0257407.png" />.
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''of a [[continuous mapping]]''
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A continuous mapping $h : f(X) \rightarrow X$ of the image $f(X)$ of a continuous mapping $f : X \rightarrow Y$ of topological spaces $X,Y$ which is a [[Section of a mapping|section]] of $f$: that is, $f \circ h$ is the identity mapping on $f(X)$.
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Latest revision as of 19:51, 22 October 2016

of a continuous mapping

A continuous mapping $h : f(X) \rightarrow X$ of the image $f(X)$ of a continuous mapping $f : X \rightarrow Y$ of topological spaces $X,Y$ which is a section of $f$: that is, $f \circ h$ is the identity mapping on $f(X)$.

How to Cite This Entry:
Continuous section. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Continuous_section&oldid=15587
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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