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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Tree-like continua and 2-to-1 maps
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by Jo Heath and Van C. Nall PDF
Proc. Amer. Math. Soc. 132 (2004), 283-289 Request permission

Abstract:

It is not known if there is a 2-to-1 map from a continuum onto a tree-like continuum. In fact, it is not known if there is a 2-to-1 map onto a hereditarily decomposable tree-like continuum. We show that the domain of such a map would have to contain an indecomposable continuum.
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Additional Information
  • Jo Heath
  • Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
  • Email: heathjw@auburn.edu
  • Van C. Nall
  • Affiliation: Department of Mathematics & Computer Science, University of Richmond, Richmond, Virginia 23173
  • Email: vnall@richmond.edu
  • Received by editor(s): November 16, 2001
  • Received by editor(s) in revised form: July 27, 2002
  • Published electronically: August 19, 2003
  • Communicated by: Alan Dow
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 283-289
  • MSC (2000): Primary 54C10
  • DOI: https://doi.org/10.1090/S0002-9939-03-06989-2
  • MathSciNet review: 2021272