I remember that there is a theorem saying that "any $C^k (k>1)$ manifold has a smooth atlas" so that, instead of consdering $C^k$ manifolds, we study smooth manifolds.

What is this theorem called and where can I find its proof?

  • 1
    $\begingroup$ Does every theorem needs to have name? $\endgroup$
    – Creator
    Aug 16, 2016 at 22:24
  • 3
    $\begingroup$ @Creator Definitely not, but I'm having trouble searching for its proof. That's why I asked whether there is a name for this theorem. Actually, I'm not sure whether the statement is correct. I just remember I heard that from someone someday, but I have no idea who it was and what exactly the statement was. $\endgroup$
    – Rubertos
    Aug 16, 2016 at 22:37
  • $\begingroup$ I think Hirsch has this. $\endgroup$
    – Aloizio Macedo
    Aug 17, 2016 at 0:46
  • $\begingroup$ For a textbook reference (Hirsch), see here. $\endgroup$ Nov 11, 2021 at 15:21

1 Answer 1


It's a result by Hassler Whitney, in one of his earlier papers on manifolds, that any maximal $C^r$ atlas, for $r>0$, contains a $C^\infty$ atlas. I can't find the specific paper at the moment, but it should be in volume I of his collected publications. My guess would be either [24] or [28] in the bibliography.

Most textbooks I know of, such as Jeffrey Lee's Manifolds and Differential Geometry, mention the result, but don't find it worth proving, so I would suggest looking for Whitney's original paper if you want to see the proof.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .