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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1195724-2
PII: S 0002-9939(1994)1195724-2
Keywords: (Weakly) (sub)metacompact, (weakly) (sub)orthocompact, infinite product, $ \Sigma $-product
Article copyright: © Copyright 1994 American Mathematical Society