Difference between revisions of "Characteristic mapping"
From Encyclopedia of Mathematics
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| − | A continuous mapping | + | A continuous mapping $\chi$ from a closed $n$-dimensional ball $E^n$ into a topological Hausdorff space $X$ that is a homeomorphism on the interior $\mathrm{int}(E^n)$ of the ball. The set $e^n = \chi[\mathrm{int}(E^n)]$ is then called a ''cell'' of $X$, and $\chi$ is called the characteristic mapping of the cell $e^n$. If $X$ is a [[cellular space]], then the cells of $X$ are defined as those cells of $X$ that form the cellular decomposition of $X$. |
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Latest revision as of 21:46, 11 November 2017
in topology
A continuous mapping $\chi$ from a closed $n$-dimensional ball $E^n$ into a topological Hausdorff space $X$ that is a homeomorphism on the interior $\mathrm{int}(E^n)$ of the ball. The set $e^n = \chi[\mathrm{int}(E^n)]$ is then called a cell of $X$, and $\chi$ is called the characteristic mapping of the cell $e^n$. If $X$ is a cellular space, then the cells of $X$ are defined as those cells of $X$ that form the cellular decomposition of $X$.
How to Cite This Entry:
Characteristic mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_mapping&oldid=14406
Characteristic mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Characteristic_mapping&oldid=14406
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article