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
DOI:
https://doi.org/10.1090/S0002-9947-1975-0375326-0
MathSciNet review:
0375326
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
Keywords:
Monotone mapping,
open mapping,
p. 1. manifold,
polyhedron
Article copyright:
© Copyright 1975
American Mathematical Society