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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Arcwise connectedness of semiaposyndetic plane continua

Author: Charles L. Hagopian
Journal: Trans. Amer. Math. Soc. 158 (1971), 161-165
MSC: Primary 54.55
MathSciNet review: 0284981
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Abstract: In a recent paper, the author proved that if a compact plane continuum $ M$ contains a finite point set $ F$ such that, for each point $ x$ in $ M - F,M$ is semi-locally-connected and not aposyndetic at $ x$, then $ M$ is arcwise connected. The primary purpose of this paper is to generalize that theorem. Semiaposyndesis, a generalization of semi-local-connectedness, is defined and arcwise connectedness is established for certain semiaposyndetic plane continua.

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Keywords: Semiaposyndesis, semi-local-connectedness, aposyndesis, arcwise connected continua, folded complementary domain
Article copyright: © Copyright 1971 American Mathematical Society