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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cellular maps between polyhedra
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by James P. Henderson PDF
Trans. Amer. Math. Soc. 272 (1982), 527-537 Request permission

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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 272 (1982), 527-537
  • MSC: Primary 57Q55; Secondary 54E60, 57N60, 57Q37
  • DOI: https://doi.org/10.1090/S0002-9947-1982-0662050-3
  • MathSciNet review: 662050