On a continuity theorem for constructive functions

2007/11/30 by Alexander Vladimirov, A. A. Vladimirov, Vladimirov, A. A.
Mathematics · #03F60 #46S30 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #math.FA #math.LO #msc:03F60 #msc:46S30

paper · pdf · doi:10.48550/arxiv.0711.4963

13 pages

arxiv created 2007/11/30 · openalex publication_date 2007/11/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

One proves that any everywhere defined constructive mapping from a complete metric space into a complete metric space which preserves the property of precompacity of subsets is locally uniformly continuous. This fact can be viewed as interpretation of L. E. J. Brower's fan theorem in terms of A. A. Markov's constructive analysis.

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