Wallman's type order compactification

Tae Choe, Young Park
1979 Pacific Journal of Mathematics  
For a completely regular ordered space X, the Stone-Cech order compactification &(X) has been constructed by Nachbin. This compactification is a generalized concept of the ordinary Stone-Cech compactification β(X) in the sense that if X has the discrete order: x ^ y iff x = y, then β ί X = βX. In this paper, for a convex ordered space X with a semi-closed order, the Wallman order compactification ω o (X) is constructed by the use of the concept of maximal bifilters. ω o (X) is a Tx-compact
more » ... ed topological space in which X is densely embedded in both the topological and order sense.
doi:10.2140/pjm.1979.82.339 fatcat:j4zijv2x5nhdtkbukzjvafuswm