- How do you define a derivative on a manifold with no metric?
Main Question or Discussion Point
I was reading about differentiable manifolds on wikipedia, and in the definition it never specifies that the differentiable manifold has a metric on it. I understand that you can set up limits of functions in topological spaces without a metric being defined, but my understanding of derivatives suggests that you need a metric in both the domain and the codomain, in order to come up with a rate of change which you are finding the limit of. Is there a more general definition of the derivative that is being used here?