- #1

- 22

- 0

My questions about problem:

1. What is topology here? (Because I need topology to show that this is manifold)

2. In solution they say that mapping x[tex]\rightarrow[/tex]{{cos x, -sin x},{sin x, cos x}} is diffeomorphism between circle and given set and from this follows that given set is manifold.

How to prove that this is diffeomorphosm? (proving by definition is pretty hard, although it's somehow obvious that this is true if use proper topology)

Diffeomorphism is special kind of mapping between two smooth manifolds - so I really don't know to show that this mapping is diffeomorphism (because before that I must show that A is smooth manifold).

3. They also say that in coords of this one dimensional smooth manifold, tangent vector is [tex]\frac{\partial}{\partial x}[/tex]?