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You use R^3 in your example of why coordinates don't matter. R^3 can be covered by one chart. Maybe your argument would be more convincing if you pick a differe
by mathgradthrow 2y ago
You use R^3 in your example of why coordinates don't matter. R^3 can be covered by one chart. Maybe your argument would be more convincing if you pick a different manifold. I have no idea what your complaint is otherwise.
- ajkjk 2y agoI'm not talking about charts of R^3; I'm talking about the different isomorphic constructions of products like ((a, b), c) and (a, (b, c)) as being a sort of 'choice of coordinate system' on the isomorphic class of objects.
- mathgradthrow 2y agoyes, and these choices dont matter individually, but how these choices glue together does, in fact, depend on all of them collectively.