Which connected spaces have a quotient homeomorphic to an arc

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 difficult...

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Bibliographic Details
Main Author Wójcik, Michał Ryszard
Format Journal Article
LanguageEnglish
Published 24.10.2014
Subjects
Mathematics - General Topology
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Summary: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.
DOI:10.48550/arxiv.1410.6655