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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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.


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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
Article copyright: © Copyright 1970 American Mathematical Society