The main objective for this thesis is the construction of a tensor bundle on a diffeological space X. Thereby getting access to the exterior bundle of antisymmetric tensors on X, and smooth sections here on i.e. differential forms. We shall list certain requirements that any reasonable tensor bundle on a diffeological space should fulfil. And show that the given construction fulfil these requir...

We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation between the first two is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient if and only if the space and the tangent fibres