Functional analysis on two-dimensional local fields

TL;DR

This paper explores the functional analytic structure of two-dimensional local fields, describing their properties as locally convex spaces and analyzing submodules such as bounded, c-compact, and compactoid ones.

Contribution

It provides a detailed functional analysis framework for two-dimensional local fields, including their description as locally convex spaces and the study of their submodules.

Findings

Characterization of two-dimensional local fields as locally convex spaces

Analysis of bounded, c-compact, and compactoid submodules within these fields

Insights into the structure and properties of these submodules

Abstract

We establish how a two-dimensional local field can be described as a locally convex space once an embedding of a local field into it has been fixed. We study the resulting spaces from a functional analytic point of view: in particular we study bounded, c-compact and compactoid submodules of two-dimensional local fields.