Discrete cells properties in the boundary set setting

Bowers, Philip L.

doi:10.1090/S0002-9939-1985-0776212-6

Discrete cells properties in the boundary set setting
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by Philip L. Bowers

Proc. Amer. Math. Soc. 93 (1985), 735-740

DOI: https://doi.org/10.1090/S0002-9939-1985-0776212-6

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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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Applications of general position properties of dendrites to Hilbert space topology

Dense embeddings of sigma-compact, nowhere locally compact metric spaces

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