Strict topoligies in non-Archimedean function spaces

Abstract

Let F be a non-trivial complete non-Archimedean valued field. Some locally F-convex topologies, on the space Cb(X,E) of all bounded continuous functions from a zero-dimensional topological space X to a non-Archimedean locally F-convex space E, are studied. The corresponding dual spaces are also investigated.