On the structure of the set of coincidence points

We consider the set of coincidence points for two maps between metric spaces. Cardinality, metric and topological properties of the coincidence set are studied. We obtain conditions which guarantee that this set (a) consists of at least two points; (b) consists of at least n points; (c) contains a countable subset; (d) is uncountable. The results are applied to study the structure of the double point set and the fixed point set for multivalued contractions. © 2015 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.