Abstract
In this paper we present a generalization of the Eilenberg-Montgomery fixed point theorem for acyclic upper semi-continuous multi-valued maps of compact metric absolute neighborhood retracts analogous to the Borsuk's extension of the Lefschetz-Hopf fixed point theorem for single-valued maps. We introduce the class of nearly extendable multi-valued maps and prove that every acyclic upper semi-continuous nearly extendable multi-valued map of arbitrary compactum having Čech homology of finite type into itself with non-trivial Lefschetz numer has a fixed point.
This paper was written while the second author was visiting University of Zagreb on leave from University of Yamaguchi.
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© 1987 Springer-Verlag
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Čerin, Z., Watanabe, T. (1987). Borsuk fixed point theorem for multi-valued maps. In: Mardešić, S., Segal, J. (eds) Geometric Topology and Shape Theory. Lecture Notes in Mathematics, vol 1283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081415
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DOI: https://doi.org/10.1007/BFb0081415
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