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On Screenability and Metrizability of Moore Spaces

Published online by Cambridge University Press:  20 November 2018

G. M. Reed
G. M. Reed*
Affiliation:
Ohio University, Athens, Ohio
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After showing that each screenable Moore space is pointwise paracompact and that the converse is not true, Heath in [4] asked for a necessary and sufficient condition for a pointwise paracompact Moore space to be screenable. In [12], Traylor asked for a necessary and sufficient condition for a pointwise paracompact Moore space to be metrizable. It is the purpose of this paper to provide such conditions, and to establish relationships between those conditions and metrization problems in Moore spaces.

A Moore space S is a space (all spaces are T1) in which there exists a sequence G = (G1, G2, …) of open coverings of S, called a development, which satisfies the first three parts of Axiom I in [7]. The statement that a collection H of subsets of the space S is point finite (point countable) means that no point of S belongs to infinitely (uncountably) many elements of H.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 6 , December 1971 , pp. 1087 - 1092
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Bing, R. H., Metrization of topological spaces, Can. J. Math. 8 (1951), 653–663.Google Scholar
2. Fitzpatrick, B., On dense subspaces of Moore spaces, Proc. Amer. Math. Soc. 16 (1965), 1324–1328.Google Scholar
3. Fitzpatrick, B., On dense subspaces of Moore spaces. II, Fund. Math. 61 (1967), 91–92.Google Scholar
4. Heath, R. W., Screenability, pointwise paracompactness and metrization of Moore spaces, Can. J. Math. 16 (1964), 763–770.Google Scholar
5. Fitzpatrick, B., Separability and\Hi-compactness, Colloq. Math. 12 (1964), 11–14.Google Scholar
6. Fitzpatrick, B., A non-pointwise paracompact Moore space with a point countable base, Notices Amer. Math. Soc. 10 (1963), 649–650.Google Scholar
7. Moore, R. L., Foundations of point set theory, Amer. Math. Soc. Colloquium Publication No. 13, Revised Edition (Amer. Math. Soc, Providence, 1962).Google Scholar
8. Fitzpatrick, B., A set of axioms for plane analysis situs, Fund. Math. 25 (1935), 13–28.Google Scholar
9. Pixley, C. and Roy, P., Uncompletable Moore spaces, Proc. of the Auburn Topology Conference, 1969, 75–85 (Auburn, Alabama).Google Scholar
10. Proctor, C. W., Metrizable subsets of Moore spaces, Fund. Math. 66 (1969), 85–93.Google Scholar
11. Reed, G. M., Concerning normality, metrizability and the Souslin property in subspaces of Moore spaces (to appear in Gen. Topology and Appl.).Google Scholar
12. Traylor, D. R., Concerning metrizability of pointwise paracompact Moore spaces, Can. J. Math. 16 (1964), 407–411.Google Scholar
13. Younglove, J. N., Concerning metric subspaces of non-metric spaces, Fund. Math. Ifi (1959), 15–25.Google Scholar