For $0<k<\infty$ and any $n$-dimensional $C^k$ manifold the maximal atlas contains a $C^\infty$ atlas on the same underlying set by a theorem due to Whitney. Could someone please point me to where I can find the theorem and a proof thereof?
2026-05-06 05:45:04.1778046304
Theorem by Whitney
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Morris Hirsch's Differential Topology text contains a proof. I don't have the text here, but it appears fairly early in the textbook. The key idea is in his theorem on increasing the order of differentiability of a function.