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Borsuk fixed point theorem for multi-valued maps

Part of the Lecture Notes in Mathematics book series (LNM,volume 1283)

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.

This paper is in final form and no version of it will be submitted for publication elsewhere.

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18443-0

  • Online ISBN: 978-3-540-47975-8

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