> Could you give me a heads-up when you are done with your first sweep?
I'm done with my first sweep.
> I'm not too keen on using that Wikipedia page as the source for the "usual definition" of smoothness for Frechet manifolds. There's a lot of details missing there.
Maybe I'll add them, or maybe we should do what you suggest:
> I usually quote the "Historical Remarks" at the end of the first chapter of Kriegl and Michor's book.
The 'standard' theory of Fréchet manifolds as in Palais' book is different from Kriegl and Michor's new approach, and Tim should probably pick one of those and talk only about that, instead of scaring my readers (who presumably are interested in fluid flow more than this foundational stuff) with two approaches.
In fact, as far as I know all the actual hard work on fluid dynamics uses Hilbert manifolds rather than Fréchet manifolds! So personally I would have stuck with Hilbert manifolds (which requires thinking about Sobolev spaces, but are otherwise more like ordinary finite-dimensional Riemannian manifolds) rather than talk about Fréchet manifolds. But of course Tim gets to do what he wants!