Monotone and open mappings onto

Author:
John J. Walsh

Journal:
Proc. Amer. Math. Soc. **60** (1976), 286-288

MSC:
Primary 54C10; Secondary 57C99

MathSciNet review:
0425888

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Abstract | References | Similar Articles | Additional Information

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 is surjective; (ii) a mapping *f* from *M* to *Y* is homotopic to an open mapping from *M* onto *Y* if and only if ) has finite index in .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1976-0425888-6

Keywords:
Open mapping,
monotone mapping,
manifold,
ANR

Article copyright:
© Copyright 1976
American Mathematical Society