Characterization of the classical extensions of the family of continuous functions as Dedekind hulls (Q610517)

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.