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- Formal proof that it does not exist a global coordinate chart on a 2-sphere

Hi,

I know there is actually

So, from a formal mathematical point of view, how to prove it ? Just because there is not a (global)

I know there is actually

*no*way to set up a global coordinate chart on a 2-sphere (i.e. we cannot find a family of 2-parameter curves on a 2-sphere such that two nearby points on it have nearby coordinate values on ##\mathbb R^2## and the mapping is one-to-one).So, from a formal mathematical point of view, how to prove it ? Just because there is not a (global)

*homeomorphism*between the 2-sphere and the Euclidean plane ##\mathbb R^2## ? Thanks.