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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 $X$.

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.)
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