Difference between revisions of "Characteristic mapping"
From Encyclopedia of Mathematics
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− | A continuous mapping | + | A continuous mapping 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