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Concerning Metrizability of Pointwise Paracompact Moore Spaces

Published online by Cambridge University Press:  20 November 2018

D. R. Traylor
D. R. Traylor*
Affiliation:
Auburn University
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Although it is known that there exists a pointwise paracompact Moore space which is not metrizable (1), very little seems to be known about the metrizability of pointwise paracompact Moore spaces. This paper is devoted to determining some of the conditions under which a pointwise paracompact Moore space is metrizable.

The statement that 5 is a Moore space means that there exists a sequence of collections of regions in 5 satisfying Axiom 0 and the first three parts of Axiom 1 of (2). A Moore space is complete if and only if it satisfies all of Axiom 1 of (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 407 - 411
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bing, R. H., Metrization of topological spaces, Can. J. Math., 3 (1951), 175–186.Google Scholar
2. Moore, R. L., Foundations of point set theory, Am. Math. Soc. Coll. Pub., 13 (1962).Google Scholar
3. Stone, A. H., Paracompactness and product spaces, Bull. Am. Math. Soc, 54 (1948), 977– 982.Google Scholar