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Spaces with differential structure and an application to cosmology

Cherenack P., Ntumba P.

Demonstratio Mathematica

2001

Vol. 34, nr 1

161-180

Categorical relations between the categories of differential, Frolicher, structured and F-structured spaces are determined and some of the forgetful functors defined on these categories are seen to be topological. The category of differential spaces is seen to be not Cartesian closed (the category of Frolicher spaces is Cartesian closed). Finally, a concrete simple example showing how the the radiation filled Robertson-Walker universe (one space dimension) has a suitable Frolicher space but not of necessity a structured space model is given.