Vol. 82, No. 2, 1979

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Wallman’s type order compactification

Tae Ho Choe and Young Soo Park

Vol. 82 (1979), No. 2, 339–347

For a completely regular ordered space X, the Stone-Čech order compactiflcation β1(X) has been constructed by Nachbin. This compactification is a generalized concept of the ordinary Stone-Čech compactiflcation β(X) in the sense that if X has the discrete order: x y iff x = y, then β1X = βX. In this paper, for a convex ordered space X with a semi-closed order, the Wallman order compactification ω0(X) is constructed by the use of the concept of maximal bifilters. ω0(X) is a T1-compact ordered topological space in which X is densely embedded in both the topological and order sense.

Mathematical Subject Classification 2000
Primary: 54D35
Received: 6 December 1976
Revised: 30 October 1978
Published: 1 June 1979
Tae Ho Choe
Young Soo Park