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 not relying on K&M's definition (due to Michal [1,2] and Bastiani [3]), but I don't how they relate (Keller [4] treats this, I think, but I don't have access to that book).

> 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

[2] Michal, A. D. _Differential of  functions with arguments and values in  topological  abelian groups_, Proc. Nat. Acad. Sci. USA **26** (1940), 356–359.

[3] Bastiani, A., _Applications differentiables et varietes differentiables de dimension infinie_, J. Anal. Math. **13** (1964), 1–114. (sorry for missing accents!)

[4] Keller, H. H., _Differential Calculus in Locally Convex Spaces_, Springer-Verlag, 1974