H-closed and countably compact extensions

John Warnock Carlson

Vol. 81 (1979), No. 2, 317–326

DOI: 10.2140/pjm.1979.81.317

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