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