Definition of "diffeological"

We apply this notion to make some observation on subspaces which split off as smooth direct summands (providing examples which illustrate that not all subspaces do), and then to show that the diffeological dual of a finite-dimensional diffeological vector space always has the standard diffeology and in particular, any pseudo-metric on the initial space induces, in the obvious way, a smooth scalar product on the dual..

2015, Ekaterina Pervova, “On the notion of scalar product for finite-dimensional diffeological vector spaces”, in arXiv‎