DIFFERENTIAL STRUCTURES FOR FUNCTION SPACES

Piotr Multarzy\'nski

Key words: Differentiable manifold; differential space;
        differential structure; space of smooth mappings;
        proper and admissible differential structures;
        structured spaces; Whitney topology.

1991 Math. Subject Classification: 58A40; 58D99; 53C99; 16W99; 83E05.

Abstract: In this paper there are presented and analyzed
different differential structures on the space of smooth mappings. It
turns out that the {\em proper} structures are especially interesting
since they are well organized by the partial order relation. Then
there are {\em admissible} structures defined and compared with the
{\em proper} structures. There are also presented differential
structures induced from the spaces of jets.