Products of WeakP‐Spaces andK‐Analytic Spaces

Abstract

Let κ be an infinite cardinal. Okuyama showed that the product space X ×i Y of a paracompact weak P (ω)‐space X and a K‐analytic space Y is paracompact. In this paper, by using the notion of κ‐K‐analytic spaces which is basically defined by Hansell, Jayne and Rogers, the above result is extended and some other results are given related to normality, collectionwise normality and covering properties on products. An answer to a question of Okuyama and Watson is also given, as well as some applications to extensions of continuous functions on these products.