# What is the manifold structure of smooth path on infinite dimensional manifolds?

What is the manifold structure of smooth path on infinite dimensional manifolds?

In the the paper "manifolds of smooth maps by Michor", it was mentioned that it is possible to put manifold structure on $$C^{\infty}(M,N)$$ for some infinite dimensional manifolds N but there is no more information. I could not find much information if M is infinite dimensioanl.

After some search I have got impression that they could be diffeology space (which is new to me) and if I am not mistaken they are not manifold.

• It is indeed a diffeological space. In general the space of smooth maps between diffeological spaces is itself a diffeological space in a very natural way. And (infinite) dimensional manifolds are in particular diffeological spaces. – Rik Voorhaar Oct 20 '19 at 14:06