The dimension of closed sets in the Stone-Čech compactification

Author:
James Keesling

Journal:
Trans. Amer. Math. Soc. **299** (1987), 413-428

MSC:
Primary 54D35; Secondary 54D40, 54F45

DOI:
https://doi.org/10.1090/S0002-9947-1987-0869420-3

MathSciNet review:
869420

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Abstract: In this paper properties of compacta in are studied for Lindelöf spaces . If , then there is a mapping such that is onto and every mapping homotopic to is onto. This implies that there is an essential family for consisting of disjoint pairs of closed sets. It also implies that if with each closed, then there is a such that .

Assume is a compactum in as above. Then if , there is a closed set in such that and such that every nonempty -set in contains an -dimensional compactum. This holds for finite or infinite. If and with each closed, then there must be a such that .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1987-0869420-3

Keywords:
Stone-Čech compactification,
Lindelöf space,
dimension,
homotopically onto,
-torus,
essential family,
sum theorem

Article copyright:
© Copyright 1987
American Mathematical Society