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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Monotone and open mappings onto $ANR’s$
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by John J. Walsh PDF
Proc. Amer. Math. Soc. 60 (1976), 286-288 Request permission

Abstract:

Let M be either a compact, connected p.l. manifold of dimension at least three or a compact, connected Hilbert cube manifold and let Y be a compact, connected ANR (= absolute neighborhood retract). The main results of this paper are: (i) a mapping f from M to Y is homotopic to a monotone mapping from M onto Y if and only if ${f_\ast }:{\pi _1}(M) \to {\pi _1}(Y)$ is surjective; (ii) a mapping f from M to Y is homotopic to an open mapping from M onto Y if and only if ${f_\ast }({\pi _1}(M))$) has finite index in ${\pi _1}(Y)$.
References
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 286-288
  • MSC: Primary 54C10; Secondary 57C99
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0425888-6
  • MathSciNet review: 0425888