Vol. 108, No. 2, 1983

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On F-spaces and F-spaces

Alan Stewart Dow

Vol. 108 (1983), No. 2, 275–284

Two problems concerning F-spaces and F-spaces are investigated. The first problem is to characterize those F-spaces whose product with every P-space is an F-space. A new necessary condition is obtained which is in fact a characterization of those F-spaces whose product with any P-space with only one non-isolated point is an F-space. As a corollary an example of a locally compact F-space and a P-space whose product is not an F-space is obtained. The second problem is to verify a conjecture of Comfort, Hindman and Negrepontis. It is shown that each weakly Lindelöf F-space is an F-space. Also, each zero-dimensional weakly Lindelöf F-space is strongly zero-dimensional.

Mathematical Subject Classification 2000
Primary: 54G05
Secondary: 54D99, 54G10
Received: 14 December 1981
Revised: 16 March 1982
Published: 1 October 1983
Alan Stewart Dow