Many geometrical features of manifolds and fibre bundles modelled on Fr chet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fr chet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Fr chet space, and the non-existence of an exponential map in a Fr chet-Lie...