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Is the reason why one can't construct global coordinate charts on manifolds in general because the topology of a given coordinate chart is that of Euclidean space (i.e. ##\mathbb{R}^{n}## with the standard topology), whereas, in general the global topology of the manifold will be much more complex?! If this is the case, can one only construct a global coordinate chart on a manifold if its global topology is the standard Euclidean topology (does Minkowski spacetime have the standard Euclidean topology with a Minkowski geometry)?!