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
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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.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