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On the functional representation of the order completion of the vector lattice of continuous functions. (Russian) Zbl 0595.46025

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

MSC:

46E05 Lattices of continuous, differentiable or analytic functions
46A40 Ordered topological linear spaces, vector lattices

Citations:

Zbl 0479.54009
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