Products of topological spaces

Abstract

The main purpose of this paper is to unify a number of theorems in topology whose conclusions state that a product of topological spaces has a compactness-like property.Three such theorems are (1) the Tychonoff theorem: Every product of compact spaces is compact, (2) the theorem of C.T. Scarborough and A.H. Stone: Every product of at most N₁ sequentially compact spaces is countably compact, and (3) the theorem of N. Noble: A countable product of Lindelöf P-spaces is Lindelöf.