Submetacompactness and Weak Submetacompactness in Countable Products, Ⅱ

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.