Characterization of the classical extensions of the family of continuous functions as Dedekind hulls
type: Item
instance of: scholarly article
title: Characterization of the classical extensions of the family of continuous functions as Dedekind hulls
zbMATH Open document ID: 1215.46017
DOI: 10.1134/S1064562406060160
published in: Doklady Mathematics
publication date: 2010-12-08T00:00:00Z
review text: 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.
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 46E05
Mathematics Subject Classification ID: 28A10
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 5824757
author: V. K. Zakharov
MaRDI profile type: Publication
cites work: Q3364069
cites work: Q5631608
cites work: Q3283133
description: scientific article; zbMATH DE number 5824757