Vol. 81, No. 2, 1979

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H-closed and countably compact extensions

John Warnock Carlson

Vol. 81 (1979), No. 2, 317–326
Abstract

Nearness structures that are generated by countably compact T1 strict extensions or H-closed extensions are characterized. For a Hausdorff topological space a compatible nearness structure is given for which the completion is the Fomin H-closed extension. A collection of compatible nearness structures for a given Hausdorff space is isolated; and it is shown that there exists a one-to-one correspondence between this collection and the collection of all strict H-closed extensions of the given space, up to the obvious equivalence.

Mathematical Subject Classification 2000
Primary: 54E17
Secondary: 54D35
Milestones
Received: 13 March 1978
Revised: 7 September 1978
Published: 1 April 1979
Authors
John Warnock Carlson