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Monotone and open mappings onto $ ANR's$


Author: John J. Walsh
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
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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)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0425888-6
Keywords: Open mapping, monotone mapping, manifold, ANR
Article copyright: © Copyright 1976 American Mathematical Society

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