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

 

Fixed points in indecomposable $ k$-junctioned tree-like continua


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 138 (2010), 1511-1515
MSC (2010): Primary 54F15, 54H25
Published electronically: November 12, 2009
MathSciNet review: 2578546
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Abstract: Let $ M$ be an indecomposable $ k$-junctioned tree-like continuum. Let $ f$ be a map of $ M$ that sends each composant of $ M$ into itself. Using an argument of O. H. Hamilton, we prove that $ f$ has a fixed point.


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Additional Information

Charles L. Hagopian
Affiliation: Department of Mathematics and Statistics, California State University, Sacra- mento, 6000 J Street, Sacramento, California 95819
Email: hagopian@csus.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10165-X
PII: S 0002-9939(09)10165-X
Keywords: Fixed point, indecomposable, composant-preserving map, $k$-junctioned, tree-like continuum.
Received by editor(s): December 4, 2008
Received by editor(s) in revised form: December 22, 2008, and August 1, 2009
Published electronically: November 12, 2009
Additional Notes: The author wishes to thank Marcus Marsh, Janusz Prajs, and the referee for suggestions that led to the improvement of this paper and Michael Heacock for drawing Figure 1.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2009 American Mathematical Society