On Metric Completness and Completness in sense of Lattices

2003/12/22 by Serguei Samborski, Samborski, Serguei
Computer Science · Mathematics · #06B30 (secondary) #46A40 #46E05 (primary) #54H12 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:06B30 #msc:46A40 #msc:46E05 #msc:54H12

paper · pdf · doi:10.48550/arxiv.math/0312410

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openalex publication_date 2003/12/22 · arxiv created 2004/05/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an answer to the following question: for which metric in an abstract lattice the completion as a metric space coincides with the completion as a lattice. We obtain the answer for inductive limits of lattices which are complete in both senses. As an application we construct such a metric in the lattice of continuous functions endowed with the uniform convergence.

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