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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Metacompactness, paracompactness, and interior-preserving open covers

Author: Heikki J. K. Junnila
Journal: Trans. Amer. Math. Soc. 249 (1979), 373-385
MSC: Primary 54D18; Secondary 54D20
MathSciNet review: 525679
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Abstract: In this paper metacompactness and paracompactness are characterized in terms of the existence of closure-preserving closed refinements and interior-preserving open star-refinements of interior-preserving directed open covers of a topological space. Several earlier results on metacompact spaces and paracompact spaces are obtained as corollaries to these characterizations. For a Tychonoff-space X, metacompactness of X is characterized in terms of orthocompactness of $ X\, \times \,\beta X$.

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Keywords: Metacompact, paracompact, interior-preserving, closure-preserving, directed cover, orthocompact, $ {M^\char93 }$-space
Article copyright: © Copyright 1979 American Mathematical Society

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