Vol. 84, No. 1, 1979

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On T1-compactifications

Somashekhar Amrith Naimpally and Mohan Lal Tikoo

Vol. 84 (1979), No. 1, 183–190
Abstract

In a recent paper [4], Reed constructed a class of T1-compactifications which generalized the well known correspondence between T2-compactifications, proximity relations and families of maximal round filters. This class includes the Wallman compactification and the one point compactification of a locally compact T1-space. In this paper the first two problems posed by Reed are solved. In particular we prove that in a nearness space the Reed compactification is equivalent to a cluster compactification. Use is made of the duality between filters and grills as developed by Thron [5].

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54E05
Milestones
Received: 18 October 1978
Revised: 2 March 1978
Published: 1 September 1979
Authors
Somashekhar Amrith Naimpally
Mohan Lal Tikoo