Weakly confluent, $2$-to-$1$ maps on hereditarily indecomposable continua
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- by Jo W. Heath PDF
- Proc. Amer. Math. Soc. 117 (1993), 569-573 Request permission
Abstract:
One of the most important open questions today in the study of exactly $2$-to-$1$ maps is whether or not such a map can be defined on the pseudoarc. We show that there is no weakly confluent $2$-to-$1$ map defined on the pseudoarc. More precisely, it is shown that any reduced weakly confluent $2$-to-$1$ map defined on a hereditarily indecomposable metric continuum must be a confluent local homeomorphism. It follows from this that if there is a weakly confluent $2$-to-$1$ map from a hereditarily indecomposable continuum $X$ onto a continuum $Y$, then neither $X$ nor $Y$ can be treelike.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 569-573
- MSC: Primary 54F15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1129879-1
- MathSciNet review: 1129879