Banach manifold

A notion of infinite-dimensional manifold. A **Banach manifold** is a manifold modelled on Banach spaces. By default, transition maps are taken to be smooth.

The category of smooth Banach manifolds has a full and faithful functor into the category of diffeological spaces. In terms of Chen smooth spaces this was observed in (Hain). For more see at *Fréchet manifold – Relation to diffeological spaces*.

For general references see at *infinite-dimensional manifold*.

The embedding into the category of diffeological spaces is discussed in

- Richard Hain,
*A characterization of smooth functions defined on a Banach space*, Proc. Amer. Math. Soc. 77 (1979), 63-67 (web, pdf)

Revised on March 6, 2015 07:40:50
by Urs Schreiber
(195.113.30.252)