The Dedekind completion of C(X): an interval-valued functions approach

Abstract

In his paper [1] R. Anguelov described the construction of the Dedekind order completion of C(X) the set of all real-valued continuous functions defined on a completely regular topological space X; using Hausdorff continuous real intervalvalued functions. The aim of this paper is to show that Anguelov’s construction can be deduced via an order isomorphism from an earlier construction  obtained by A. Horn in [8].

Quaestiones Mathematicae 34(2011), 213–223.