Bump-Functions on Certain Infinite Dimensional Manifolds

Let A be a unitary commutative complete locally m-convex C ^*-algebra. We prove that the projective finitely generated A-modules admit differentiable A-valued bump-functions. Then we consider manifolds modelled on such modules and we prove that locally defined differentiable mappings and sections on these manifolds extend to global ones. This revised version was published online in June 2006 with corrections to the Cover Date.