Open Access

Two topological definitions of a Nielsen number for coincidences of noncompact maps

Fixed Point Theory and Applications20042004:480951

Received: 25 August 2003

Published: 3 March 2004


The Nielsen number is a homotopic invariant and a lower bound for the number of coincidences of a pair of continuous functions. We give two homotopic (topological) definitions of this number in general situations, based on the approaches of Wecken and Nielsen, respectively, and we discuss why these definitions do not coincide and correspond to two completely different approaches to coincidence theory.

Authors’ Affiliations

Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, Czech Republic
Department of Mathematics, University of Würzburg, Würzburg, Germany
Fachbereich Mathematik und Informatik (WE1), Freie Universität Berlin, Arnimallee 2-6, Germany


© Andres and Väth 2004