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 | References | Similar Articles | Additional Information
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.
- F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 379–382. MR 69888, DOI https://doi.org/10.1073/pnas.41.6.379
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999
- Harry T. Mathews, The $n$-arc property for functions meromorphic in the disk, Math. Z. 93 (1966), 164–170. MR 218572, DOI https://doi.org/10.1007/BF01111035
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Keywords:
Homeomorphism of the disk,
<IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">-separated-arc property,
ambiguous point
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© Copyright 1970
American Mathematical Society