Dedekind order completion of \(C(X)\) by Hausdorff continuous functions. (English) Zbl 1062.54017

Anguelov, R.

Quaest. Math. 27, No. 2, 153-169 (2004).

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 \(X\).

Reviewer: Ryszard Pawlak (Łódź)

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.)

Keywords:

Hausdorff continuous; interval valued function; Dedekind completion