Locally convex structures on higher local fields
  We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In particular, we study bounded and compactoid submodules of these fields and establish a self-duality result once a suitable topology on the dual space has been introduced. 
Alberto Camara
math.NT math.AG math.FA