Vol. 65, No. 2, 1976

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A class of T1-compactifications

Ellen Elizabeth Reed

Vol. 65 (1976), No. 2, 471–484

In this work the correspondence between T2-compactifications, proximity relations, and families of maximal round filters is extended to the case of T1-spaces. The major results spell out bijections between a special class of T1-compactifications, certain proximity relations on the original space, and certain filterfamilies. Perhaps the most interesting result is the identification of a class of compactifications between T1 and T2-compactifications. This class consists of the principal weakly regular minimal compactifications and includes the Wallman compactification, and also the one-point compactification of a locally compact space. Moreover, the Wallman compactification is the largest weakly regular minimal compactification of a T1-space. This improves the known result that the Wallman compactification is T1, and is larger than any T2-compactification.

Mathematical Subject Classification 2000
Primary: 54D35
Secondary: 54E05
Received: 22 March 1976
Revised: 16 June 1976
Published: 1 August 1976
Ellen Elizabeth Reed