Wallman’s type order compactification

Tae Ho Choe and Young Soo Park

Vol. 82 (1979), No. 2, 339–347

DOI: 10.2140/pjm.1979.82.339

Abstract

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

Milestones

Received: 6 December 1976

Revised: 30 October 1978

Published: 1 June 1979