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

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On the existence of exactly $(2,1)$ maps
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by R. E. Smithson
Proc. Amer. Math. Soc. 99 (1987), 577-580
DOI: https://doi.org/10.1090/S0002-9939-1987-0875403-5

Abstract:

The following two theorems concerning the existence of exactly 2 to 1 maps are proved. If $Y$ is a continuum such that each nondegenerate subcontinuum contains a cutpoint, then there does not exist a continuum $X$ and an exactly 2 to 1 map on $X$ onto $Y$. Further, if $X$ is an arcwise connected continuum and $Y$ is a nested continuum, then there does not exist an exactly 2 to 1 map on $X$ onto $Y$.
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Bibliographic Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 577-580
  • MSC: Primary 54F15; Secondary 54C10, 54F20, 54F50
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0875403-5
  • MathSciNet review: 875403