A generalized inductive limit strict topology on the space of bounded continuous functions ✩

A generalized inductive limit strict topology β∞ is defined on Cb(X, E), the space of all bounded, continuous functions from a zero-dimensional Hausdorff space X into a locally K-convex space E, where K is a field with a nontrivial and nonarchimedean valuation, for which K is a complete ultrametric space. Many properties of the topology β∞ are proved and the dual of (Cb (X, E), β∞) is studied.