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

 

Tree-like continua with invariant composants under fixed-point-free homeomorphisms


Authors: C. L. Hagopian, M. M. Marsh and J. R. Prajs
Journal: Proc. Amer. Math. Soc. 140 (2012), 3655-3661
MSC (2010): Primary 54F15, 54H25
Published electronically: May 9, 2012
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Abstract: Using an example of D. P. Bellamy, we define a 3-composant tree-like continuum admitting a fixed-point-free homeomorphism that sends each composant onto itself. This continuum is used to define an indecomposable tree-like continuum that admits a composant-preserving fixed-point-free homeomorphism. A map extension theorem is proved and applied in this construction.


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Additional Information

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

M. M. Marsh
Affiliation: Department of Mathematics and Statistics, California State University, Sacramento, 6000 J Street, Sacramento, California 95819
Email: mmarsh@csus.edu

J. R. Prajs
Affiliation: Department of Mathematics and Statistics, California State University, Sacramento, 6000 J Street, Sacramento, California 95819
Email: prajs@csus.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11727-7
PII: S 0002-9939(2012)11727-7
Keywords: Fixed point, indecomposable, composant-preserving map, $k$-junctioned, tree-like continuum
Received by editor(s): December 8, 2010
Published electronically: May 9, 2012
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.