Étude des espaces vectoriels topologiques et applications sur les jauges et les tonneaux

This bachelor's thesis provides a rigorous exploration of the foundamental structures at intersection of linear algebra and general topology. The aim of this work is to synthesize the essential properties of topological vector spaces (TVS), with a specific focus on set-theoretic geometry: convex, absorbing, balanced and closed sets. This in-depth study demonstrates how the concept of Minkowski functional and barrel serve as pivotal tools for characterizing the continuity and structure of locally convex spaces, establishing the necessary groundwork for research in many fields of mathematics such as functional analysis and operator theory.