Fixed points in indecomposable junctioned treelike continua
Author:
Charles L. Hagopian
Journal:
Proc. Amer. Math. Soc. 138 (2010), 15111515
MSC (2010):
Primary 54F15, 54H25
Published electronically:
November 12, 2009
MathSciNet review:
2578546
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Abstract: Let be an indecomposable junctioned treelike continuum. Let be a map of that sends each composant of into itself. Using an argument of O. H. Hamilton, we prove that has a fixed point.
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 D. P. Bellamy, A treelike continuum without the fixed point property, Houston J. Math. 6 (1980), 113. MR 575909 (81h:54039)
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 R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119132. MR 0236908 (38:5201)
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 C. L. Hagopian, The fixedpoint property for almost chainable homogeneous continua, Illinois J. Math. 20 (1976), 650652. MR 0418057 (54:6101)
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 C. L. Hagopian, The fixedpoint property for deformations of treelike continua, Fundamenta Math. 155 (1998), 161176. MR 1606519 (99b:54046)
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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/S000299390910165X
Keywords:
Fixed point,
indecomposable,
composantpreserving map,
$k$junctioned,
treelike 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
