Comment by mathgradthrow
1 year 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.
I'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.
yes, and these choices dont matter individually, but how these choices glue together does, in fact, depend on all of them collectively.