2014/06/25 by Enxin Wu, Wu, Enxin · 2 citations
Mathematics · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research
paper · pdf · doi:10.48550/arxiv.1406.6717
Diffeological spaces are natural generalizations of smooth manifolds, introduced by J.M.~Souriau and his mathematical group in the 1980's. Diffeological vector spaces (especially fine diffeological vector spaces) were first used by P. Iglesias-Zemmour to model some infinite dimensional spaces in~\citeI1,I2. K.~Costello and O.~Gwilliam developed homological algebra for differentiable diffeological vector spaces in Appendix A of their book~\citeCG. In this paper, we present homological algebra of general diffeological vector spaces via the projective objects with respect to all linear subductions, together with some applications in analysis.