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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.


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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