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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dendrites and light mappings
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by Janusz J. Charatonik and Paweł Krupski PDF
Proc. Amer. Math. Soc. 132 (2004), 1211-1217 Request permission


It is shown that a metric continuum $X$ is a dendrite if and only if for every compact space (continuum) $Y$ and for every light confluent mapping $f: Y \to f(Y)$ such that $X \subset f(Y)$ there is a copy $X’$ of $X$ in $Y$ for which the restriction $f|X’: X’ \to X$ is a homeomorphism. As a corollary it follows that only dendrites have the lifting property with respect to light confluent mappings. Other classes of mappings $f$ are also discussed. This is a continuation of a previous study by the authors (2000), where open mappings $f$ were considered.
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Additional Information
  • Janusz J. Charatonik
  • Affiliation: Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
  • Email:
  • Paweł Krupski
  • Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Email:
  • Received by editor(s): March 14, 2001
  • Received by editor(s) in revised form: February 4, 2002
  • Published electronically: October 29, 2003
  • Communicated by: Alan Dow
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1211-1217
  • MSC (2000): Primary 54C60, 54C65, 54E40, 54F50
  • DOI:
  • MathSciNet review: 2045440