The dimension of closed sets in the StoneČech compactification
Author:
James Keesling
Journal:
Trans. Amer. Math. Soc. 299 (1987), 413428
MSC:
Primary 54D35; Secondary 54D40, 54F45
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:
http://dx.doi.org/10.1090/S00029947198708694203
PII:
S 00029947(1987)08694203
Keywords:
StoneČech compactification,
Lindelöf space,
dimension,
homotopically onto,
torus,
essential family,
sum theorem
Article copyright:
© Copyright 1987
American Mathematical Society
