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 interval-valued 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].