On Fixed-Point Free Selections and Multivalued Maps on R

Authors

  • Dennis K. Burke Miami University
  • Raushan Buzyakova

DOI:

https://doi.org/10.4995/agt.2015.2291

Keywords:

fixed-point free map, hyperspace, multivalued map

Abstract

We study fixed-point free multivalued selfmaps on R as well as continuous fixed-point free selection of multivalued selfmaps on R. We justify necessary conditions in some earlier results and motivate some new interesting questions.

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Author Biography

Dennis K. Burke, Miami University

Department of Mathematics

References

J. M. Aarts, R. J. Fokkink and J. Vremeer, Variations on a theorem of Lusternik and Schnirelmann, Topology 35 (1996), 1051-1056. https://doi.org/10.1016/0040-9383(95)00057-7

N. G. de Bruijn and P. Erdös, A color problem for infinite graphs and a problem in the theory of relations, Indagationes Math. 13 (1951), 371-373. https://doi.org/10.1016/S1385-7258(51)50053-7

R. Buzyakova, On multivalued fixed-point free maps on $R^n$, Proc. Amer. Math. Soc. 140 (2012), 2929-2936. https://doi.org/10.1090/S0002-9939-2011-11166-3

R. Buzyakova and A. Chigogidze, Fixed-point free maps of Euclidean spaces, Fundamenta Mathematicae, 212 (2011), 1-16. https://doi.org/10.4064/fm212-1-1

R. Engelking, General Topology, PWN, Warszawa, 1977. J. van Mill, The infinite-dimensional topology of function spaces, Elsevier, Amsterdam, 2001.

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Published

2015-01-28

How to Cite

[1]
D. K. Burke and R. Buzyakova, “On Fixed-Point Free Selections and Multivalued Maps on R”, Appl. Gen. Topol., vol. 16, no. 1, pp. 31–36, Jan. 2015.

Issue

Section

Regular Articles