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arXiv · 1302.2935

The D-topology for diffeological spaces

J. Daniel Christensen·Gord Sinnamon·Enxin Wu
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Abstract

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.

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J. Daniel Christensen, Gord Sinnamon, Enxin Wu. 2013-02-12. The D-topology for diffeological spaces. https://doi.org/10.2140/pjm.2014.272.87

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