A fixed point theorem and equivariant points for set-valued mappings

Abstract

We give a proof of a coincidence theorem for a Vietoris mapping and a compact mapping and prove the Lefschetz fixed point theorem for the class of admissible mappings which contains upper semi-continuous acyclic mappings. When a source space is a paracompact Hausdorff space with a free involution and a target space is a closed topological manifold with an involution, the existence of equivariant points is proved for the class of admissible mappings under some conditions. When a source space is a Poincaré space with a finite covering dimension, the covering dimension of the set of equivariant points is determined.