I can see why their exists some \(\displaystyle C^{\infty}\) structure. Just define \(\displaystyle \Omega\) to be the set of all atlases on \(\displaystyle X\) containing \(\displaystyle \mathfrak{A}\), order it in the natural way and apply Zorn's lemma. But, why is it unique? Is it because the way one constructs the ordering any two maximal atlases \(\displaystyle \mathfrak{M},\mathfrak{N}\) would need to be comparable and thus equal?

Any help would be appreciated!