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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Cellular maps between polyhedra


Author: James P. Henderson
Journal: Trans. Amer. Math. Soc. 272 (1982), 527-537
MSC: Primary 57Q55; Secondary 54E60, 57N60, 57Q37
MathSciNet review: 662050
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Abstract: A compact subset $ X$ of a polyhedron $ P$ is cellular in $ P$ if there is a pseudoisotopy of $ P$ shrinking precisely $ X$ to a point. A proper surjection $ f:P\rightarrow Q$ is cellular if each point inverse of $ f$ is cellular in $ P$. We give certain conditions under which cellular maps between polyhedra are approximable by homeomorphisms. An example of a cellular map which is not approximable by homeomorphisms is also given.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0662050-3
Keywords: Cellular map, polyhedron, approximation, stratification
Article copyright: © Copyright 1982 American Mathematical Society