Abstract
In this paper, we shall discuss submetacompactness and weak submetacompactness in countable products of Čech-scattered spaces and prove the following: (1) If $\{ X_{n} : n \in \omega \}$ is a countable collection of submetacompact Čech-scattered spaces, then the product $\Prod_{n\in \omega} X_{n}$ is submetacompact. (2) If $Y$ is a hereditarily weakly submetacompact space and $\{X_{n} : n \in \omega \}$ is a countable collection of weakly submetacompact Čech-scattered spaces, then the product $Y \times \Prod_{n\in \omega}X_{n}$ is weakly submetacompact.
Citation
Hidenori Tanaka. "Submetacompactness and Weak Submetacompactness in Countable Products, Ⅱ." Tsukuba J. Math. 32 (1) 139 - 154, June 2008. https://doi.org/10.21099/tkbjm/1496165194
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