O przestrzeniach Banacha

Abstract

The structure of the world, as reconstructed by contemporary physics, is made out of mathematical functions. Functional spaces, which are standard tools of theoretical physics, are usually Banach spaces. Their nature, as generalization of vector spaces, is briefly presented. It turns out that Banach spaces appear not only in foundations of physics (for example, in a rigorous treatment of the least action principle) but also in a modelling of the very process of physical theories development. Is this a trivial consequence of our convention to describe the world in terms of functions and of the fact that Banach spaces are nice functional spaces or has this fact a deeper philosophical meaning?