Talk:Existence of Local Coordinates

I am doubting this theorem is true. For example, $S^2$ (the sphere in $\R^3$) is a neighbourhood of any of its points, but does not admit global coordinates.

I would say the correct statement is (but then, this is how a manifold is defined in the first case):
 * 'For any point $p\in X$, there is a neighbourhood $U$ such that $U$ admits local coordinates.'

Any thoughts? --Lord_Farin 08:46, 24 October 2011 (CDT)


 * Sorry - so far over my head I can't hear it whistle. --prime mover 17:11, 24 October 2011 (CDT)