The $n$-separated-arc property for homeomorphisms
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- by C. L. Belna
- Proc. Amer. Math. Soc. 24 (1970), 98-99
- DOI: https://doi.org/10.1090/S0002-9939-1970-0249626-X
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Abstract:
Let $f$ be a function defined in the open unit disk $D$ whose range is in the Riemann sphere $W$, and let $C$ denote the unit circle. We show that if $f$ is a homeomorphism of $D$ onto a Jordan domain, then the set of points $p \in C$ at which $f$ has the $n$-separated-arc property $(n \geqq 2)$ is a subset of the set of ambiguous points of $f$ and is thus countable.References
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- Harry T. Mathews, The $n$-arc property for functions meromorphic in the disk, Math. Z. 93 (1966), 164–170. MR 218572, DOI 10.1007/BF01111035
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 24 (1970), 98-99
- MSC: Primary 30.62
- DOI: https://doi.org/10.1090/S0002-9939-1970-0249626-X
- MathSciNet review: 0249626