Fixed Point Theory and Applications
Volume 2004 (2004), Issue 1, Pages 49-69
doi:10.1155/S1687182004308119
Two topological definitions of a Nielsen number for coincidences of noncompact maps
Jan Andres1
and Martin Väth2
1Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, Olomouc-Hej {c}ín 779 00, Czech Republic
2Department of Mathematics, University of Würzburg, Am Hubland, Würzburg D-97074, Germany
Abstract
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.