A fixed point theorem for inverse limits of fans
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- by M. M. Marsh PDF
- Proc. Amer. Math. Soc. 91 (1984), 139-142 Request permission
Abstract:
In [1] David Bellamy gave an example of a tree-like continuum without the fixed point property. Another example of a tree-like continuum which admits a fixed point free mapping was given in [5] by L. G. Oversteegen and J. T. Rogers, Jr. We prove in this paper that a certain inverse limit of fans has the fixed point property. Certain possible methods for simplifying Bellamy’s and Oversteegen and Roger’s examples are eliminated by our theorem.References
- David P. Bellamy, A tree-like continuum without the fixed-point property, Houston J. Math. 6 (1980), no. 1, 1–13. MR 575909 —, An example of a tree-like continuum without the fixed point property, Proc. Internat. Conf. on Geometric Toplogy, PWN, Warsaw, 1980, pp. 35-38.
- Charles L. Hagopian, The fixed-point property for almost chainable homogeneous continua, Illinois J. Math. 20 (1976), no. 4, 650–652. MR 418057
- K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
- Lex G. Oversteegen and James T. Rogers Jr., Fixed-point-free maps on tree-like continua, Topology Appl. 13 (1982), no. 1, 85–95. MR 637430, DOI 10.1016/0166-8641(82)90010-4
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 139-142
- MSC: Primary 54F20
- DOI: https://doi.org/10.1090/S0002-9939-1984-0735580-0
- MathSciNet review: 735580