Which connected spaces have a quotient homeomorphic to an arc

2014/10/24 by Michał Ryszard Wójcik, Wójcik, Michał Ryszard
Mathematics · #54B15 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GN #msc:54B15

paper · pdf · doi:10.48550/arxiv.1410.6655

arxiv created 2014/10/24 · openalex publication_date 2014/10/24 · arxiv updated 2014/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We announce and examine the conjecture that each infinite connected normal Hausdorff space has a quotient homeomorphic to the unit interval, shown to be true with the additional assumption of compactness or local connectedness. Some connected subsets of the plane are considered to show the difficulties involved in developing a general argument.

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