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F′-spaces and z-embedded subspaces
Mark Mandelker |
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Vol. 28 (1969), No. 3, 615–621
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Abstract |
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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
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Milestones
Received: 3 April 1968
Revised: 8 July 1968
Published: 1 March 1969
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Authors |
| Mark Mandelker | |
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