Differentiable manifolds modelled on locally convex spaces

Abstract

We construct differentiable manifolds modelled on locally convex spaces using Yamamuro ' s theory of Γ-differentiation [81], [ 82] , manifolds which we term as Γ-manifolds . Then corresponding to the strong notion of BΓ-differentiability in Yamamuro ' s theory [82] we obtain the subclass of BΓ-manifolds . We show how to extend to these BΓ-manifolds the standard properties of Banach manifolds : The Smale Density Theorem [4] as well as the Transversality Theory [4]; [ 31] . As first applications , we give several simple results about genericity of smooth maps using our Γ-technique instead of the usual standard Banach techniques .