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Proceedings of the American Mathematical Society

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



Proper hereditary shape equivalences preserve small weak infinite-dimensionality

Author: Richard P. Millspaugh
Journal: Proc. Amer. Math. Soc. 110 (1990), 1055-1061
MSC: Primary 54F45; Secondary 54C10
MathSciNet review: 1037215
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Abstract: A space is said to be small weakly infinite dimensional if it has a basis $ B$ such that the collection of finite unions of elements of $ B$ is inessential. A characterization of small weak infinite dimensionality is given for locally compact spaces. This characterization is then used to prove that if $ f:X \to Y$ is a proper hereditary shape equivalence from a metric space $ X$ which is small weakly infinite dimensional onto a locally compact metric space $ Y$, then $ Y$ is small weakly infinite dimensional.

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Keywords: Small weakly infinite dimensional, hereditary shape equivalence, approximately invertible map, inessential
Article copyright: © Copyright 1990 American Mathematical Society