TheD-topology for diffeological spaces

John Daniel Christensen, Gordon Sinnamon, Enxin Wu
2014 Pacific Journal of Mathematics  
Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural topology called the D-topology. However, the D-topology has not yet been studied seriously in the existing literature. In this paper, we develop the basic theory of the D-topology for diffeological spaces. We explain that the topological spaces that arise as the D-topology of a diffeological space are exactly the
more » ... erated spaces and give results and examples which help to determine when a space is Δ-generated. Our most substantial results show how the D-topology on the function space C^∞(M,N) between smooth manifolds compares to other well-known topologies.
doi:10.2140/pjm.2014.272.87 fatcat:coxfiwjztzbu3lbleoaavdwjj4