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Proceedings of the American Mathematical Society

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The $ n$-separated-arc property for homeomorphisms


Author: C. L. Belna
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
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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 [Enhancements On Off] (What's this?)

  • [1] F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 379-382. MR 16, 1095. MR 0069888 (16:1095d)
  • [2] E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Math. and Math. Phys., no. 56, Cambridge Univ. Press, Cambridge, 1966. MR 38 #325. MR 0231999 (38:325)
  • [3] H. T. Mathews, The $ n$-arc property for functions meromorphic in the disk, Math. Z. 93 (1966), 164-170. MR 36 #1657. MR 0218572 (36:1657)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0249626-X
Keywords: Homeomorphism of the disk, $ n$-separated-arc property, ambiguous point
Article copyright: © Copyright 1970 American Mathematical Society

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