# Problem Sheet B

- Problem 1 is a linear analogue of the notion of a smooth atlas on a manifold.
- Problem 2 gives (yet) another way to think about the tangent space, this time via equivalence classes of charts and vectors.
- Problem 3 asks you to show that the dash-to-dot maps are behave nicely with respect to linear maps.
- Problem 4 asks you to prove that the cotangent bundle is a smooth manifold.
- Problems 5-7 are about point-set topological counterexamples.

Comments and questions?