I originally posted this question on StackExchange, where it was suggested I post here. It was also suggested I read about Hilbert manifolds and Fréchet manifolds. Nevertheless, I …

Consider a bounded domain $S\subset R^2$ and an elliptic system of two first order PDEs, namely a generalization of the Cauchy-Riemann system allowing nonconstant coefficients and …

Let $M$ and $N$ be closed manifolds. Is it true that $C^{k}(N,M)$, which is the space of functions $f: N\to M$ such that $f\in C^{k}$, is a $C^{\infty}$ Banach manifold? If so, c …

After reading this MO post, I am wondering: Is every (connected) Hausdorff Banach manifold a regular space? Though unjustified, page 53 of this paper nonchalantly states: "Note …

This question stems from Jeff Rubin's earlier MO question and a follow-up that I posted. The former recalls the following result proved by both Serge Lang (Fundamentals of Differ …

Is there a notion of "smooth bundle of Hilbert spaces" (the base is a smooth finite dimensional manifold, and the fibers are Hilbert spaces) such that: 1• A smooth bundle …

In the introduction to 'A convenient setting for Global Analysis', Michor & Kriegl make this claim: "The study of Banach manifolds per se is not very interesting, since they tu …

I'm pretty sure that this is a minor error, but I could use some help here. So the book I'm referring to in the title is this book (MR1164870). On pg. 16-17, he is proving that th …

Let $X$ be a Frechet or Banach manifold. We can define tangent vectors by equivalence classes of smooth curves. But, we could also define them as derivations of germs of smooth fun …