The D-topology for diffeological spaces

By J. Christensen, Gord Sinnamon, Enxin Wu. 2013

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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 $\Delta$-generated spaces and give results and examples which help to determine when a space is $\Delta$-generated. Our most substantial results show how the $D$-topology on the function space $C^{\infty}(M,N)$ between smooth manifolds compares to other well-known topologies.

Subfields: Geometry and Topology, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/33023a06a38196f42c64f5bd1a80a4a616f24ec6