Bornological spaces of non-Archimedean valued functions

Abstract

Let C(X,E) be the space of all continuous functions from an ultraregular space X to a non-Archimedean locally convex space E. Necessary and/or sufficient conditions are given so that C(X,E), with the topology of uniform convergence on compact sets or with the topology of simple convergence, is bornological or c-ultrabornological.