- #71
PeterDonis
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TrickyDicky said:For a differentiable manifold the structure is preserved by diffeomorphisms between the manifold's subset and Euclidean space."
I just can't see how a diffeomorphism is possible between a single chart in GR covering the whole manifold and Euclidean space.
A diffeomorphism preserves the differentiable structure, but that is not the same as the metric. Preserving the metric is a much stronger condition than just preserving the differentiable structure.