On the submetacompactness of products

Yajima, Yukinobu

doi:10.1090/S0002-9939-1989-0942639-6

On the submetacompactness of products
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by Yukinobu Yajima

Proc. Amer. Math. Soc. 107 (1989), 503-509

DOI: https://doi.org/10.1090/S0002-9939-1989-0942639-6

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Abstract:

In this paper, we raise the question of whether the product $X \times Y$ of a regular space $X$ with a $\sigma$-closure-preserving cover by compact sets and a submetacompact space $Y$ is submetacompact, and we show that the product $X \times Y$ is weakly submetacompact.

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