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Some Results on Weak Covering Conditions

Published online by Cambridge University Press:  20 November 2018

Raymond F. Gittings
Raymond F. Gittings*
Affiliation:
University of Pittsburgh, Pittsburgh, Pennsylvania; Brooklyn College, Brooklyn, New York
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A space X is called countdbly metacompact (countably paracompact) if every countable open cover has a point finite (locally finite) open refinement. According to Hodel [5], a space X is called countably subparacompact if every countable open cover has a σ-discrete closed refinement. It is well-known (see Mansfield [10] and Dowker [4]) that in normal spaces all of the preceding notions are equivalent. Also, according to Hodel [5], a countably subparacompact space is countably metacompact and the reverse implication is false.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1152 - 1156
Copyright
Copyright © Canadian Mathematical Society 1974

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