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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Uniquely arcwise connected plane continua have the fixed-point property


Author: Charles L. Hagopian
Journal: Trans. Amer. Math. Soc. 248 (1979), 85-104
MSC: Primary 54F20
MathSciNet review: 521694
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Abstract: This paper contains a solution to a fixed-point problem of G. S. Young [17, p. 884] and R. H. Bing [4, Question 4, p. 124]. Let M be an arcwise connected plane continuum that does not contain a simple closed curve. We prove that every continuous function of M into M has a fixed point.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0521694-X
PII: S 0002-9947(1979)0521694-X
Keywords: Fixed-point property, uniquely arcwise connected continua, plane continua, indecomposable continua, Warsaw circle
Article copyright: © Copyright 1979 American Mathematical Society