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Widely-connected sets in the bucket-handle continuum

Volume 240 / 2018

David Lipham Fundamenta Mathematicae 240 (2018), 161-174 MSC: 54D05, 54F15, 54F50, 54E50, 54G20. DOI: 10.4064/fm378-3-2017 Published online: 4 August 2017


A connected topological space is said to be widely-connected if each of its non-degenerate connected subsets is dense in the entire space. The object of this paper is the construction of widely-connected subsets of the plane. We give a completely metrizable example that answers a question of Paul Erdős and Howard Cook, while a similar example answers a question of Jerzy Mioduszewski.


  • David LiphamDepartment of Mathematics and Statistics
    Auburn University
    Auburn, AL 36849, U.S.A.

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