Differential forms on differentiable spaces

Abstract

In |5| we have defined the category of N-differentiable (not necessarily reduced) spaces and have described certain subcategories that seem to be of special interest. For one of these restricted categories we have, for example, established certain embedding theorems of the classical type for manifolds. At this point then one should describe certain constructions to "smooth” differentiable spaces, so that starting with a general space, one ends with a space in a more restricted, but nicer class. By this we are able, for example, to extend certain embedding results of |5| to a far more general class of differentiable spaces (see |7|).