Automatic continuity of biseparating maps

2001/06/13 by Jesús Araujo, Jesus Araujo, Araujo, Jesus +2
Mathematics · #46E25 (Secondary) #46E40 #47B33 (Primary) 46H40 #47B38 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.FA #msc:46E25 #msc:46E40 #msc:46H40 #msc:47B33 #msc:47B38

paper · pdf · doi:10.48550/arxiv.math/0106106

8 pages; no figures

arxiv created 2001/06/13 · openalex publication_date 2001/06/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when it is not true.

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