In a lecture about differential geometry my teacher presented the following theorem:
Theorem (Whitney). Any $C^k$- atlas $\mathcal{A}_{C^{k}}$ (with $k \geq 1$) of a topological manifold contains a $C^\infty$ - atlas.
However, when I searched for Whitney's theorems I only found his embedding theorems and no relation whatsoever to the theorem stated above. So here are my questions: How is the theorem above related to Whitney's embedding theorems? Are they equivalent?