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Differentiability, Convenient Spaces and Smooth Diffeologies

Carlos A. Torre
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Abstract

We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient iff the space and the tangent fibres coincide. Some basic comments on the relation with manifolds are given.

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Carlos A. Torre. 2001-12-04. Differentiability, Convenient Spaces and Smooth Diffeologies. https://arxiv.org/abs/math/0112036

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