The [nLab casually remarks](http://ncatlab.org/nlab/show/diffeological+space#References) that locally convex tvs embed into diffeological spaces by (discussion around) a corollary in Kriegl and Michor, namely 3.14, but this deals with [Boman's theorem](http://ncatlab.org/nlab/show/Boman%27s+theorem) and results about smooth maps from a euclidean space to a locally convex spaces.

The definition of smoothness for maps $U \to V$ where $U$ is $c^\infty$-open in a lctvs $W$, and $V$ is a lctvs, is given so that smooth maps are automatically the same as between maps between the associated diffeological spaces.

However, there is a notion of smoothness for maps between lctvs (due to Michal [1,2] and Bastiani [3]) not relying on K&M's definition, but I don't how they relate (Keller [4] treats this, I think, but I don't have access to that book at the moment).

> Is it still true that lctvs embed into diffeological spaces using Michal-Bastiani smoothness?


[1] Michal, A. D. _Differential calculus in linear topological spaces_, Proc. Nat. Acad. Sci. USA **24** (1938), 340-342 ([pdf](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1077109/pdf/pnas01796-0040.pdf))

[2] Michal, A. D. _Differential of  functions with arguments and values in  topological  abelian groups_, Proc. Nat. Acad. Sci. USA **26** (1940), 356–359. ([pdf](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1078188/pdf/pnas01616-0038.pdf))

[3] Bastiani, A., _Applications différentiables et variétés différentiables de dimension infinie_, J. Anal. Math. **13** (1964), 1–114. ([article](http://dx.doi.org/10.1007/BF02786619), paywalled)

[4] Keller, H. H., _Differential Calculus in Locally Convex Spaces_, Lecture Notes in Mathematics 417, Springer-Verlag, 1974 ([Springerlink](http://dx.doi.org/10.1007/BFb0070564), paywalled)