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Proceedings of the American Mathematical Society

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

 

 

Tree-like continua and exactly $ k$-to-$ 1$ functions


Author: Jo Heath
Journal: Proc. Amer. Math. Soc. 105 (1989), 765-772
MSC: Primary 54C10; Secondary 54F50
MathSciNet review: 936775
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0936775-8
Keywords: $ k$-to-$ 1$ function, $ 2$-to-$ 1$ function, tree-like continua
Article copyright: © Copyright 1989 American Mathematical Society