Namespaces
Variants
Actions

Difference between revisions of "Continuous section"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(Tex done)
 
Line 1: Line 1:
−
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" />.
+
''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 a mapping|section]] of $f$: that is, $f \circ h$ is the identity mapping on $f(X)$.
 +
 
 +
{{TEX|done}}

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=39496
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=Continuous_section&oldid=39496"