Locally convex structures on higher local fields

Abstract

Higher local fields can be described as locally convex vector spaces once an embedding of a local field into them has been fixed. This extends previous two-dimensional results of the author. We study these spaces in the framework of nonarchimedean functional analysis. In particular, we introduce new classes of bounded and compactoid submodules and establish a self-duality result once the dual space has been suitably topologized.