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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Monotone and open mappings on manifolds. I


Author: John J. Walsh
Journal: Trans. Amer. Math. Soc. 209 (1975), 419-432
MSC: Primary 57A15; Secondary 54C10
MathSciNet review: 0375326
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Abstract: Sufficient conditions are given for the existence of open mappings from a p. 1. manifold $ {M^m},m \geqslant 3$, onto a polyhedron $ Q$. In addition, it is shown that a mapping $ f$ from $ {M^m},m \geqslant 3$, to $ Q$ is homotopic to a monotone mapping of $ M$ onto $ Q$ iff $ {f_ \ast }:{\pi _1}(M) \to {\pi _1}(Q)$ is onto. Finally, it is shown that a monotone mapping of $ {M^m},m \geqslant 3$, onto $ Q$ can be approximated by a monotone open mapping of $ M$ onto $ Q$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0375326-0
PII: S 0002-9947(1975)0375326-0
Keywords: Monotone mapping, open mapping, p. 1. manifold, polyhedron
Article copyright: © Copyright 1975 American Mathematical Society