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Locally Compact Normal Spaces in the Constructible Universe

Published online by Cambridge University Press:  20 November 2018

W. Stephen Watson
W. Stephen Watson*
Affiliation:
University of Toronto, Toronto, Ontario
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Arhangel'skiĭ proved around 1959 [1] that, for the class of perfectly normal locally compact spaces, metacompactness and paracompactness are equivalent. It is shown to be consistent that this equivalence holds for the (larger) class of normal locally compact spaces (answering a question of Tall [8], [9]).

The consistency of the existence of locally compact normal noncollectionwise Hausdorff spaces has been known since 1967. It is shown that the existence of such spaces is independent of the axioms of set theory, thus establishing that Bing's example G cannot be modified under ZFC to be locally compact.

All topological spaces are assumed to be Hausdorff.

First, a definition and three standard lemmata are needed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 5 , 01 October 1982 , pp. 1091 - 1096
Copyright
Copyright © Canadian Mathematical Society 1982

References

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