Vol. 303, No. 1, 2019

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Diffeological vector spaces

J. Daniel Christensen and Enxin Wu

Vol. 303 (2019), No. 1, 73–92
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.

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Keywords
diffeological vector space, homological algebra, fine diffeology, projective diffeological vector space, smooth linear functionals
Mathematical Subject Classification 2010
Primary: 46S99
Secondary: 57P99
Milestones
Received: 6 May 2017
Revised: 29 January 2019
Accepted: 27 February 2019
Published: 21 December 2019
Authors
J. Daniel Christensen
Department of Mathematics
University of Western Ontario
London ON
Canada
Enxin Wu
Department of Mathematics
Shantou University
Guangdong
China