- #51

- 30,053

- 9,241

Yes, I agree with that.I'm saying that a bare manifold, a manifold without a metric, still admits coordinates.

But, once again, how do you know that the coordinate labels ##x^a + dx^a## and ##y^a + dy^a## label the same point ##Q##?In particular two overlapping coordinate systems and points ##P## and ##Q##, which to start off with we consider abstarctly, can be labelled in the two coordinates systems and in general ##dx^a \not= dy^a##.