Lecture 6

Applications of the Theorem that π1(S1) is infinite cyclic (pp. 31--34)

State and prove the following:

Theorem 1.8 (Fundamental Theorem of Algebra)
Theorem 1.10 (Borsuk-Ulam Thorem)
Corollary 1.11
Proposition 1.12 (π1 of a product) (also state π1 of the torus)