Characterization of the classical extensions of the family of continuous functions as Dedekind hulls
The author considers the problem of the relationship between the family of all continuous functions on a topological space and families of measurable functions. He solves the problem in terms of order. He introduces a new property of extensions and he proves that all classical extensions, being saturated, are regular. This enables him to prove that the completeness, being boundary, and regularity conditions determine a unique extension (up to isomorphism). As a consequence, he obtains characterizations of some classical results.
scientific article; zbMATH DE number 5824757