Turn in 3 problems from Section 1.3 and the extra problems (A-D) below, and read Section 1.3

Disclaimer: You should do all of the suggested problems on your own, and I will assume that you do. I would recommend (for the midterm, final, and qualifying exams) that you do many other problems. I am available for help.

Due Wednesday, February 11.

Suggested problems:

Section 1.3 # 10, 12, 14, 16

A. Show that the quotient map \(S^2 \to \mathbb{R}P^2\) is a covering map. This will help on number 14.

B. Prove this. Let \(p:\widetilde{X}\to X\) be a covering space. The cardinality \(\#p^{-1}(x)\) of the fiber over a point is locally constant. If \(X\) is connected, this is globally constant.

C. Construct a two-sheeted covering of the Klein bottle by the torus.