Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Orthocompactness in infinite product spaces

Authors: Nobuyuki Kemoto and Yukinobu Yajima
Journal: Proc. Amer. Math. Soc. 120 (1994), 591-596
MSC: Primary 54B10; Secondary 54D20
MathSciNet review: 1195724
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Abstract: In this paper, we prove the following results for an infinite product space $ X = \prod\nolimits_{\alpha \in \kappa } {{X_\alpha }} $.

(1) If a dense subspace of $ X$ is orthocompact, then it is $ \kappa $-metacompact.

(2) Assume that all finite subproducts of $ X$ are hereditarily orthocompact. If a subspace of $ X$ is $ \kappa $-metacompact, then it is orthocompact.

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Keywords: (Weakly) (sub)metacompact, (weakly) (sub)orthocompact, infinite product, $ \Sigma $-product
Article copyright: © Copyright 1994 American Mathematical Society