Vol. 303, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
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.

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