Abstract:In this paper, we discuss covering properties in countable products of \v Cech-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 \v Cech-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 \v Cech-scattered spaces, then the product $\prod _{n\in \omega }X_n$ is metacompact.
Keywords: countable product, C-scattered, \v Cech-scatterd, subparacompact, metacompact
AMS Subject Classification: Primary 54B10, 54D15, 54D20, 54G12