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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The $ 3$-dimensionality of certain codimension-$ 3$ decompositions


Author: R. J. Daverman
Journal: Proc. Amer. Math. Soc. 96 (1986), 175-179
MSC: Primary 54B15; Secondary 54C56, 54F45, 55M10, 57N15
MathSciNet review: 813833
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Abstract: It is proved that if $ p$ is a proper mapping of an $ (n + 3)$-manifold $ M$ onto a metric space $ B$ such that each inverse set $ {p^{ - 1}}b$ has the shape of a closed, connected, orientable $ n$-manifold, then $ B$ is $ 3$-dimensional.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0813833-7
PII: S 0002-9939(1986)0813833-7
Keywords: Cohomological dimension, upper semicontinuous decomposition, proper map, codimension-$ 3$ manifold
Article copyright: © Copyright 1986 American Mathematical Society