On Fixed-Point Free Selections and Multivalued Maps on R

Dennis K. Burke, Raushan Buzyakova

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.


Keywords

fixed-point free map; hyperspace; multivalued map

Subject classification

54H25; 58C30; 54B20

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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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Universitat Politècnica de València

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