Abstract. Smooth bundles, whose fibres are distribution spaces, are introduced according to the notion of smoothness due to Froelicher. Some fundamental notions of differential geometry, such as tangent and jet spaces, Froelicher-Nijenhuis bracket, connections and curvature, are suitably generalized. It is also shown that a classical connection on a finite-dimensional bundle naturally determines a connection on an associated distributional bundle.
AMSclassification. 46F99, 53C05, 58B10, 58C99
Keywords. Generalized sections, Froelicher smoothness, connections