On the product of two topological spaces

AbstractThe thrust of the paper is toward answering “What conditions on X and Y are sufficient to insure that X × Y has property Q?” Important results by section are 3. Suppose X is subcompact (has a σ-discrete closed cover of compact subsets). If X is collectionwise normal and Y is paracompact (metacompact, screenable), then X × Y is paracompact (metacompact, screenable). If X is T2 and Y is subparacompact, then X × Y is subparacompact. 4. Let X be metrizable and Y have the Gδ-property. If Y is screenable (metacompact, subparacompact), then X × Y is screenable (metacompact, subparacompact). 5. The product of a T2, paracompact, sequential space with a countably compact, normal space is collectionwise normal. 6. X × Y is an F-product if X is T2, paracompact, and sequential while Y is countably compact and normal, or if X is collectionwise normal and subcompact while Y is paracompact and normal