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Zbl 1062.54017
Anguelov, R.
Dedekind order completion of $C(X)$ by Hausdorff continuous functions. (English)
[J] Quaest. Math. 27, No. 2, 153-169 (2004). ISSN 1607-3606; ISSN 1927-933X/e

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 $X$.
[Ryszard Pawlak (\Lódź)]

MSC 2000:: *54C35 Function spaces (general topology)
54C30 Real-valued functions on topological spaces
26E25 Set-valued real functions
35F20 General theory of first order nonlinear PDE
54D35 Compactifications

Keywords: Hausdorff continuous; interval valued function; Dedekind completion

Cited in: Zbl 1244.54042

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