Covering properties in countable products, II

summary:In this paper, we discuss covering properties in countable products of Čech-scattered spaces and prove the following: (1) If $Y$ is a perfect subparacompact space and $\{X_n : n\in \omega \}$ is a countable collection of subparacompact Čech-scattered spaces, then the product $Y\times \prod_{n\in \omega }X_n$ is subparacompact and (2) If $\{X_n : n\in \omega \}$ is a countable collection of metacompact Čech-scattered spaces, then the product $\prod_{n\in \omega }X_n$ is metacompact