Diffeological vector spaces
Differential Geometry
2019-12-25 v2
Abstract
We study the relationship between many natural conditions that one can put on a diffeological vector space: being fine or projective, having enough smooth (or smooth linear) functionals to separate points, having a diffeology determined by the smooth linear functionals, having fine finite-dimensional subspaces, and having a Hausdorff underlying topology. 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, and use our results to study the homological algebra of diffeological vector spaces.
Cite
@article{arxiv.1703.07564,
title = {Diffeological vector spaces},
author = {J. Daniel Christensen and Enxin Wu},
journal= {arXiv preprint arXiv:1703.07564},
year = {2019}
}
Comments
14 pages; to appear in Pacific J. Math