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Transactions of the American Mathematical Society

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A Periodic Point Free Homeomorphism
of a Tree-Like Continuum

Author: Piotr Minc
Journal: Trans. Amer. Math. Soc. 348 (1996), 1487-1519
MSC (1991): Primary 54F15; Secondary 54F20
MathSciNet review: 1321584
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Abstract: An example of a homeomorphism without periodic points is constructed on a tree-like continuum.

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

  • 1. D. P. Bellamy, A tree-like continuum without the fixed-point property, Houston J. Math. 6 (1980), 1--13. MR 81h:54039
  • 2. R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119--132. MR 38:5201
  • 3. K. Borsuk, Sur un continu acyclique qui se laisse transformer topologiquement en lui même sans points invariants, Fund. Math. 24 (1935), 51--58.
  • 4. K. Borsuk, Theory of shape, Polish Scientific Publishers, Warsaw, Poland, 1975. MR 54:6132
  • 5. J. H. Case and R. E. Chamberlin, Characterizations of tree-like continua, Pacific J. Math. 10 (1960), 73--84. MR 22:1868
  • 6. H. Cook, W. T. Ingram and A. Lelek, Eleven annotated problems about continua, Open Problems in Topology, North--Holland, Amsterdam, 1990, pp. 295--302. MR 91:03
  • 7. H. Cook, W. T. Ingram and A. Lelek, A list of problems known as Houston problem book, Continua with the Houston problem book, Lecture Notes in Pure and Appl. Math., Vol. 170, Marcel Dekker, New Yor, 1995, pp. 365--398. CMP 95:11
  • 8. J. B. Fugate and L. A. Mohler, A note on fixed points in tree--like continua, Topology Proc. 2 (1977), 457--460. MR 80k:54062
  • 9. C. L. Hagopian, A fixed-point theorem for tree-like continua, Topology Proc. 16 (1991), 57--62. MR 94a:54106
  • 10. W. Lewis, Continuum theory problems, Topology Proc. 8 (1983), 361--394. MR 86a:54038
  • 11. P. Minc, A tree-like continuum admitting fixed point free maps with arbitrarily small trajectories, Topology and its Appl. 46 (1992), 99--106. MR 94a:54108
  • 12. L. G. Oversteegen and J. T. Rogers, Jr., Tree-like continua as limits of cyclic graphs, Topology Proc. 4 (1979), 507--515. MR 82c:54032
  • 13. L. G. Oversteegen and J. T. Rogers, Jr., An inverse limit description of an atriodic tree-like continuum and an induced map without a fixed point, Houston J. Math. 6 (1980), 549--564. MR 82j:54075
  • 14. L. G. Oversteegen and J. T. Rogers, Jr., Fixed-point-free maps on tree-like continua, Topology and its Appl. 13 (1982), 85--95. MR 83b:54044
  • 15. R. B. Sher, Realizing cell-like maps in Euclidean space, General Topology and its Appl. 2 (1972), 75--89. MR 46:2683

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Additional Information

Piotr Minc
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849

Keywords: Tree-like continuum, periodic points
Received by editor(s): March 8, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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