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Open retractions of indecomposable continua

Volume 148 / 2017

Sumiki Fukaishi, Eiichi Matsuhashi Colloquium Mathematicum 148 (2017), 191-194 MSC: Primary 54F15; Secondary 54C10. DOI: 10.4064/cm6912-7-2016 Published online: 24 February 2017

Abstract

We show that for each continuum $X$ there exist an indecomposable continuum $Y$ which contains $X$ and an open retraction $r: Y \to X$ such that each fiber of $r$ is homeomorphic to the Cantor set. Furthermore, $Y$ is homeomorphic to the closure of a countable union of topological copies of $X$ in some continuum. This result is a strengthening of a result proved by Bellamy (1971).

Authors

  • Sumiki FukaishiDepartment of Mathematics and Computer Science
    Shimane University
    Matsue, Shimane 690-8504, Japan
    e-mail
  • Eiichi MatsuhashiDepartment of Mathematics and Computer Science
    Shimane University
    Matsue, Shimane 690-8504, Japan
    e-mail

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