F^′-spaces and their product with P-spaces

W. Wistar (William) Comfort, Neil Hindman and Stelios A. Negrepontis

Vol. 28 (1969), No. 3, 489–502

DOI: 10.2140/pjm.1969.28.489

Abstract

The F′-spaces studied here, introduced by Leonard Gillman and Melvin Henriksen, are by definition completely regular Hausdorff spaces in which disjoint cozero-sets have disjoint closures. The principal result of this paper gives a sufficient condition that a product space be an F′-space and shows that the condition is, in a strong sense, best possible. A fortuitous corollary in the same vein responds to a question posed by Gillman: When is a product space basically disconnected (in the sense that each of its cozero-sets has open closure)?

Mathematical Subject Classification

Primary: 54.20

Milestones

Received: 12 December 1967

Revised: 20 March 1968

Published: 1 March 1969