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

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... ed topological space in which X is densely embedded in both the topological and order sense.