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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Tree-like continua and exactly $k$-to-$1$ functions
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by Jo Heath
Proc. Amer. Math. Soc. 105 (1989), 765-772
DOI: https://doi.org/10.1090/S0002-9939-1989-0936775-8

Abstract:

To answer a question of Nadler and Ward, $k$-to-$1$ maps from tree-like continua onto tree-like continua are constructed, for $k > 2$. It is shown that certain arc-like continua cannot be the domain of any $2$-to-$1$ map and that certain tree-like continua cannot be the image of any $2$-to-$1$ map (defined on continua) but it is unknown if any indecomposable arc-like continuum can be the domain or any tree-like continuum the image of a $2$-to-$1$ map.
References
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Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 765-772
  • MSC: Primary 54C10; Secondary 54F50
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0936775-8
  • MathSciNet review: 936775