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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
DOI: https://doi.org/10.1090/S0002-9939-2012-11727-7
Published electronically: May 9, 2012
MathSciNet review: 2929033
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. D. Bellamy, A tree-like continuum without the fixed point property, Houston Journal Math. 6 (1979), 1-14. MR 575909 (81h:54039)
  • 2. J. B. Fugate and L. Mohler, A note on fixed points in tree-like continua, Topology Proceedings 2 (1977), 457-460. MR 540622 (80k:54062)
  • 3. C. L. Hagopian, Fixed points of arc-component-preserving maps, Trans. Amer. Math. Soc. 306 (1988), 411-420. MR 927698 (89d:54022)
  • 4. C. L. Hagopian, The fixed-point property for deformations of tree-like continua, Fundamenta Math. 155 (1998), 161-176. MR 1606519 (99b:54046)
  • 5. C. L. Hagopian, Fixed points in indecomposable k-junctioned tree-like continua, Proc. Amer. Math. Soc. 138 (2010), 1511-1515. MR 2578546 (2011d:54054)
  • 6. S. Macías, Topics on Continua (2005), Chapman and Hall/CRC, Boca Raton, London, New York, Singapore. MR 2147759 (2006f:54035)
  • 7. T. Maćkowiak and E. D. Tymchatyn, Continuous mappings on continua. II, Dissert. Math. 225 (1984), 1-57. MR 739739 (87a:54048)
  • 8. P. Minc, A tree-like continuum admitting fixed point free maps with arbitrarily small trajectories, Topology Appl. 46 (1992), 99-106. MR 1184108 (94a:54108)
  • 9. P. Minc, A hereditarily indecomposable tree-like continuum without the fixed-point property, Trans. Amer. Math. Soc. 352 (2000), 643-654. MR 1695031 (2000k:54029)

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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: https://doi.org/10.1090/S0002-9939-2012-11727-7
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.

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