An internal characterization of paracompact -spaces

Author:
R. A. Stoltenberg

Journal:
Trans. Amer. Math. Soc. **196** (1974), 249-263

MSC:
Primary 54D20

DOI:
https://doi.org/10.1090/S0002-9947-1974-0346746-4

MathSciNet review:
0346746

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Abstract: The purpose of this paper is to characterize paracompact *p*-spaces in terms of spaces with refining sequences . A space *X* has a refining sequence if there exists a sequence of open covers for *X* such that is compact for each compact subset *C* of *X* and is a neighborhood base for . If for each compact subset *C* of *X* then *X* is metrizable. On the other hand if we restrict the set *C* to the family of finite subsets of *X* in the above definition then we have a characterization for strict *p*-spaces. Moreover, in this case, if for all such sets then *X* is developable. Thus the concept of a refining sequence is natural and it is helpful in understanding paracompact *p*-spaces.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0346746-4

Keywords:
Metric spaces,
paracompact *p*-spaces,
developable spaces,
sequences of open covers,
subparacompact spaces

Article copyright:
© Copyright 1974
American Mathematical Society