Covering properties in countable products (Q1327655)

A space \(X\) is subparacompact (metacompact, respectively) provided that every open cover of \(X\) has a \(\sigma\)-discrete closed (point finite open, respectively) refinement. This paper studies conditions under which these and other covering properties are preserved by taking countable products. The key condition needed is a property called \({\mathcal D} {\mathcal C}\)-like, which is defined by using a topological game, and which involves closed sets that have discrete covers by compact subsets. Results in this paper include: a countable product of regular subparacompact (metacompact, respectively) \({\mathcal D} {\mathcal C}\)-like spaces is subparacompact (metacompact, respectively).