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Diffeological vector spaces

Research paper by J. Daniel Christensen, Enxin Wu

Indexed on: 22 Mar '17Published on: 22 Mar '17Published in: arXiv - Mathematics - Differential Geometry



Abstract

We study the relationship between many natural conditions that one can put on a diffeological vector space, including being fine or projective, having enough smooth (or smooth linear) functions to separate points, having a diffeology determined by the smooth linear functionals, and more. Our main result is that the majority of the conditions fit into a total order. We also give many examples in order to show which implications do not hold.