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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Homological embedding properties of the fibers of a map and the dimension of its image
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by John J. Walsh PDF
Proc. Amer. Math. Soc. 85 (1982), 135-138 Request permission

Abstract:

A relationship is established between the homological codimension of the point inverses of a map and the dimension of its image. An infinite-dimensional version leads to the conclusion that the image of a proper map defined on Hilbert space cannot be countable dimensional. A finite-dimensional version yields: if $g:{M^n} \to Y$ is a proper map, ${M^n}$ is a $G$-orientable $n$-manifold without boundary, and $\dim Y \leqslant k$, then there is a point $y \in Y$ and an integer $i \geqslant n - k$ such that $\check {H}^i (g^{-1}(y);G) \ne 0$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 135-138
  • MSC: Primary 54F45; Secondary 55M10, 58B05
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0647912-0
  • MathSciNet review: 647912