Vol. 28, No. 3, 1969

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F-spaces and z-embedded subspaces

Mark Mandelker

Vol. 28 (1969), No. 3, 615–621
Abstract

A completely regular Hausdorff space is an F-space if disjoint cozero-sets have disjoint closures. Here the theory of prime z-filters is applied to the study of F-spaces. A z-embedded subspace is one in which the zero-sets are all intersections of the subspace with zero-sets in the larger space. It is shown that every z-embedded subspace of an F-space is also an F-space. Also, a new characterization of F-spaces is obtained: Every z-embedded subspace is C-embedded in its closure.

Mathematical Subject Classification
Primary: 54.53
Secondary: 46.00
Milestones
Received: 3 April 1968
Revised: 8 July 1968
Published: 1 March 1969
Authors
Mark Mandelker