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Two topological definitions of a Nielsen number for coincidences of noncompact maps
Fixed Point Theory and Applications volume 2004, Article number: 480951 (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.
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Andres, J., Väth, M. Two topological definitions of a Nielsen number for coincidences of noncompact maps. Fixed Point Theory Appl 2004, 480951 (2004). https://doi.org/10.1155/S1687182004308119