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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 T 1) in which there exists a sequence G = (G 1, G 2, …) 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.

Information

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

References

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