## 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:

 54C35 Function spaces in general topology 54C30 Real-valued functions in general topology 26E25 Set-valued functions 35F20 Nonlinear first-order PDEs 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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