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Peripheral Covering Properties Imply Covering Properties

Published online by Cambridge University Press:  20 November 2018

E. E. Grace
E. E. Grace*
Affiliation:
Arizona State University, Tempe, Arizona
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Recently several papers (11; 12; 13; 14) have been published in which it is shown that a Moore space (normal, in one case) is metrizable if it has the peripheral version (in the sense defined below) of a certain covering property that was known to imply metrizability of Moore spaces. Each of these metrization theorems can be proved more easily by using a slight variation of the appropriate standard proof to show that such a space is collectionwise normal and hence (2, Theorem 10) metrizable. But this approach, as well as that followed in (11 ; 12; 13 ; 14), obscures the point that, in Moore spaces and in more general settings, the peripheral versions of these covering properties imply the covering properties.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 257 - 263
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This work was supported in part by the National Science Foundation.

References

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