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A characterization of submetacompactness in terms of products

Author: Yukinobu Yajima
Journal: Proc. Amer. Math. Soc. 112 (1991), 291-296
MSC: Primary 54D20; Secondary 54B10
MathSciNet review: 1054165
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Abstract: A space $ X$ is said to be suborthocompact if for every open cover $ \mathcal{U}$ of $ X$ there is a sequence $ \{ {\mathcal{V}_n}\} $ of open refinements of $ \mathcal{U}$ such that for each $ x \in X$ there is some $ n \in \omega $ such that $ \cap \{ V \in {\mathcal{V}_n}:x \in V\} $ is a neighborhood of $ x$ in $ X$. It is proved that a Tychonoff space $ X$ is submetacompact if and only if the product $ X \times \beta X$ is suborthocompact.

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Keywords: Submetacompact, suborthocompact, product, metacompact, directed cover, cushioned refinement
Article copyright: © Copyright 1991 American Mathematical Society

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