Basic non-Archimedean functional analysis over non-Archimedean field c #. Applications to constructive quantum field theory.

Functional analysis works with TVS (Topological Vector Spaces), classically over archimedean fields like and .Canonical non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers p etc. are fundamental, is a fast-growing discipline. This paper deals with TVS over non-classical non-Archimedean fields