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Proceedings of the American Mathematical Society

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



Discrete cells properties in the boundary set setting

Author: Philip L. Bowers
Journal: Proc. Amer. Math. Soc. 93 (1985), 735-740
MSC: Primary 57N20
MathSciNet review: 776212
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Abstract: Let $ X$ be the complement of a $ \sigma - Z$-set in a locally compact separable ANR. It is proved that $ X$ satisfies the discrete $ n$-cells property for each nonnegative integer $ n$ if and only if $ X$ satisfies the discrete approximation property. As a consequence, Hilbert space manifolds that arise as complements of boundary sets in Hilbert cube manifolds are characterized in terms of their homological structure coupled with a minimal amount of general positioning.

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Keywords: Discrete approximation property, discrete $ n$-cells property
Article copyright: © Copyright 1985 American Mathematical Society

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