Countable paracompactness in product spaces

Abstract

The main purpose of this paper is to show that X ω {X^\omega } is normal if and only if (1) X n {X^n} is normal for each n, and (2) X ω {X^\omega } is countably paracompact. Furthermore, X ω {X^\omega } is perfectly normal if and only if X ω {X^\omega } is hereditarily countably paracompact. Also, the compact Hausdorff space X is metrizable if and only if X 3 {X^3} is hereditarily countably paracompact.