Universal connections in Fréchet principal bundles

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector space, we endow the bundle JP of 1-jets of the sections of a Fréchet principal bundle P with a connection form by means of which we may “reproduce” every connection of P .