Editing Smooth structure (section)

== Related structures ==

The smoothness requirements on the transition functions can be weakened, so that the transition maps are only required to be <math>k</math>-times continuously differentiable; or strengthened, so that the transition maps are required to be real-analytic. Accordingly, this gives a [[Differential manifold|<math>C^k</math>]] or [[Analytic manifold|(real-)analytic structure]] on the manifold rather than a smooth one. Similarly, a [[Complex manifold|complex structure]] can be defined by requiring the transition maps to be holomorphic.