Metacompactness, paracompactness, and interior-preserving open covers

Junnila, Heikki J. K.

doi:10.1090/S0002-9947-1979-0525679-9

Metacompactness, paracompactness, and interior-preserving open covers
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by Heikki J. K. Junnila

Trans. Amer. Math. Soc. 249 (1979), 373-385

DOI: https://doi.org/10.1090/S0002-9947-1979-0525679-9

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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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