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Dedekind order completion of C(X) by Hausdorff continuous functions. (English) Zbl 1062.54017
In this paper the author considers the problem of constructing a Dedekind order completion of C(X) through functions defined on the same space X. Hence it contains the Dedekind order completion of the set C(X) as well as the Dedekind order completion of the set C b (X), where C b (X) means the family of all bounded continuous functions defined on X.

MSC:
54C35Function spaces (general topology)
54C30Real-valued functions on topological spaces
26E25Set-valued real functions
35F20General theory of first order nonlinear PDE
54D35Extensions of topological spaces (compactifications, supercompactifications, completions, etc.)