Homological embedding properties of the fibers of a map and the dimension of its image

Author:
John J. Walsh

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

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Abstract | References | Similar Articles | Additional Information

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 is a proper map, is a -orientable -manifold without boundary, and , then there is a point and an integer such that .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0647912-0

Keywords:
-set,
infinite codimension,
countable dimensional,
homological embedding properties,
dimension,
Hilbert space,
Hilbert cube

Article copyright:
© Copyright 1982
American Mathematical Society