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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Another fixed point theorem for plane continua


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 31 (1972), 627-628
MathSciNet review: 0286093
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Abstract: A continuum $ M$ is said to be $ \lambda $ connected if every two points of $ M$ can be joined by a hereditarily decomposable subcontinuum of $ M$. Here we prove that a bounded plane continuum that does not have infinitely many complementary domains is $ \lambda $ connected if and only if its boundary does not contain an indecomposable continuum. It follows that every $ \lambda $ connected bounded nonseparating subcontinuum of the plane has the fixed point property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0286093-6
PII: S 0002-9939(1972)0286093-6
Keywords: The fixed point property, arcwise connectedness, $ \lambda $ connected continua, hereditarily decomposable boundary, nonseparating plane continua
Article copyright: © Copyright 1972 American Mathematical Society