Jeff Rubin <JeffBRubin@gmail.com> wrote: > > I'm hesitant to assume regularity since not only Lang but AMR also doesn't > assume it. I feel like I'm missing something obvious.
Usually, also paracompactness is assumed (and I think also Lang usually assumes it, maybe he forgot one place here). In this case, there is no difficulty with regularity, of course.
If you find an answer whether a Banach (or Riemannian) manifold is automatically regular (if just the Hausdorff property but no paracompactness is assumed), please post it. This does not seem to be an easy problem.