Construction of A Lattice on the completion space of an algebra and an isomorphism to its Caratheodory Extension

2008/06/18 by Jun Tanaka, Tanaka, Jun, Peter F. McLoughlin +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0806.2940

openalex publication_date 2008/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we will show how the Caratheodory Extension process is intimately related to the metric completion process. In particular, it will be shown how one is able to construct a lattice on the completion and to obtain an isomorphism to its Caratheodory Extension.

Related

• An isomorphism between the completion of an Algebra and its Caratheodory Extension
• Amalgamating poset extensions and generating free lattices
• A Carathéodory's Extension Theorem for Families Simpler Than an Algebras of Sets
• A categorical proof of the Carathéodory extension theorem
• On Metric Completness and Completness in sense of Lattices