A Note on the Fixed Point Property of Non-metric Tree-Like Continua
DOI:
https://doi.org/10.5644/SJM.04.1.12Keywords:
Continuum, fixed point property, inverse systemAbstract
The main purpose of this paper is to study the fixed point property of non-metric tree-like continua. It is proved, using the inverse systems method, that if $X$ is a non-metric tree-like continuum and if $h:X\rightarrow X$ is a periodic homeomorphism, then $h$ has the fixed point property (Theorem 2.4). Some theorems concerning the fixed point property of arc-like non-metric continua are also given.
2000 Mathematics Subject Classification. Primary 54H25, 54F15; Secondary 54B35
Downloads
References
A. Chigogidze, Inverse spectra, Elsevier, 1996.
E. Dyer, A fixed point theorem, Proc. Am. Math. Soc., 7 (1956), 662–672.
R. Engelking, General Topology, PWN, Warszawa, 1977.
J. B. Fugate and T. B. McLean, Compact groups of homeomorphisms on tree-like continua, Trans. Am. Math. Soc., 267 (1981), 609–620.
O. H. Hamilton, A fixed point property for pseudo-arcs and certain other metric continua, Proc. Am. Math. Soc., 2 (1951), 173–174.
A. Illanes and S. B. Nadler, Jr., Hyperspaces : Fundamentals and Recent Advances, Marcel Dekker, Inc., New York and Basel, 1999.
I. Lonˇcar, A fan X admits a Whitney map for C(X) iff it is metrizable, Glas. Mat. Ser. III, 38 (58) (2003), 395–411.
I. Lonˇcar, The fixed point property for arc component preserving mappings of nonmetric tree-like continua, Math. Commun., 10 (2005), 15–21.
S. Mardeˇsi´c, Chainable continua and inverse limits, Glas. Mat. Fiz. i Astr., 14 (1959), 219–232.
J. van Mill, Infinite-Dimensional Topology, Elsevier Sci. Pub., 1989.
S. B. Nadler, Jr., Continuum Theory, Marcel Dekker, New York, 1992.
L. E. Ward, A fixed point theorem, Amer. Math. Montly, 65 (1958), 271–272.
