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 such that the collection of finite unions of elements of is inessential. A characterization of small weak infinite dimensionality is given for locally compact spaces. This characterization is then used to prove that if is a proper hereditary shape equivalence from a metric space which is small weakly infinite dimensional onto a locally compact metric space , then is small weakly infinite dimensional.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1037215-1

Keywords:
Small weakly infinite dimensional,
hereditary shape equivalence,
approximately invertible map,
inessential

Article copyright:
© Copyright 1990
American Mathematical Society