The strict topology in non-Archimedean vector-valued function spaces

AbstractLet F be a non-trivial complete non-Archimedean valued field. We study the strict topology β0 on the space Cb(X,E) of all bounded continuous functions from a topological space X to a non-Archimedean F-locally convex space E over F. We also show that the dual of the space (Cb(X,E), βo) is a certain space of E′-valued measures and we give a characterization of the equicontinuous subsets of this dual space