Fixed point in uniform spaces

Abstract

In this work, we expand some definitions of functional analysis usually defined on metric spaces to non-metric topologiqual spaces. To do so, we introduce some notions associated with nonmetrizable spaces, wich extanded the topological structures of these spaces, for make them fairly close of those of the metric spaces. It concerns some topological vector spaces of uniform structure; particularly those generated by family of semi-norms. Specially, we study the extension of the Banach contraction principle on such spaces.