Orthocompactness in infinite product spaces

Kemoto, Nobuyuki; Yajima, Yukinobu

doi:10.1090/S0002-9939-1994-1195724-2

Orthocompactness in infinite product spaces
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by Nobuyuki Kemoto and Yukinobu Yajima PDF

Proc. Amer. Math. Soc. 120 (1994), 591-596 Request permission

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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