Its a function that eats points in a manifold and spits out (linear functions that eat (linear functions satisfying Leibniz rule that eat (differentiable functions that eats points on a manifold and spit outs real numbers) and spits out real numbers) and spits out real numbers), obviously.
So what would be this mysterious everywhere-valid interpretation of dx?
Its a function that eats points in a manifold and spits out (linear functions that eat (linear functions satisfying Leibniz rule that eat (differentiable functions that eats points on a manifold and spit outs real numbers) and spits out real numbers) and spits out real numbers), obviously.
Of course!