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Proceedings of the American Mathematical Society

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A note on Jones' function $ K$


Author: John Rosasco
Journal: Proc. Amer. Math. Soc. 49 (1975), 501-504
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1975-0367946-X
MathSciNet review: 0367946
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Abstract: For each point $ x$ of a continuum $ M$, F. B. Jones [5, Theorem 2] defines $ K(x)$ to be the closed set consisting of all points $ y$ of $ M$ such that $ M$ is not aposyndetic at $ x$ with respect to $ y$. Suppose $ M$ is a plane continuum and for any positive real number $ \epsilon $ there are at most a finite number of complementary domains of $ M$ of diameter greater than $ \epsilon $. In this paper it is proved that for each point $ x$ of $ M$, the set $ K(x)$ is connected.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0367946-X
Keywords: Jones' function $ K$, aposyndesis, folded complementary domain, nonlocally connected plane continua
Article copyright: © Copyright 1975 American Mathematical Society