Veksler, A. I. On the functional representation of the order completion of the vector lattice of continuous functions. (Russian) Zbl 0595.46025 Sib. Mat. Zh. 26, No. 6(154), 159-162 (1985). The author here describes a representation of the K-completion \(\tilde X\) of \(X=C^*(T)\) (the vector lattice of all continuous bounded real valued functions on a completely regular space T) satisfying the following properties: i) \(X\subset \tilde X\) and \(\tilde X\) consists of a set of functions (or equivalence classes of functions) on T. ii) If T be extremally disconnected, then \(\tilde X=X.\) The author’s description is a slight modification of the results of V. Zaharov [Bull. Acad. Pol. Sci., Ser. Sci. Math. 29, 199-203 (1981; Zbl 0479.54009)]. Reviewer: T.K.Mukherjee Cited in 1 ReviewCited in 1 Document MSC: 46E05 Lattices of continuous, differentiable or analytic functions 46A40 Ordered topological linear spaces, vector lattices Keywords:K-completion; completely regular space Citations:Zbl 0479.54009 PDFBibTeX XMLCite \textit{A. I. Veksler}, Sib. Mat. Zh. 26, No. 6(154), 159--162 (1985; Zbl 0595.46025) Full Text: EuDML