Vol. 28, No. 3, 1969

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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

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
Received: 12 December 1967
Revised: 20 March 1968
Published: 1 March 1969
W. Wistar (William) Comfort
Neil Hindman
Stelios A. Negrepontis