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Proceedings of the American Mathematical Society

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

 

 

A class of arcwise connected continua


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 30 (1971), 164-168
MSC: Primary 54.55
DOI: https://doi.org/10.1090/S0002-9939-1971-0281164-1
MathSciNet review: 0281164
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Abstract: It is known that every bounded semi-aposyndetic plane continuum which does not separate the plane is arcwise connected. To show that this theorem remains true if the phrase ``does not separate the plane'' is replaced by ``does not have infinitely many complementary domains'' is the primary purpose of this paper.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0281164-1
Keywords: Arcwise connected continua, aposyndesis, semi-aposyndesis, cut point, complementary domain, Jones's cyclic property
Article copyright: © Copyright 1971 American Mathematical Society