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

Abstract

A generalized inductive limit strict topology β ∞ is defined on C b( 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 ( C b ( X, E), β ∞) is studied.