Lecture 10

Ch. 2, sec. 8

Prove Lemma 8.1 and Theorem 8.2. Define the notions of homotopy equivalence and homotopy type. Deduce Theorem 8.3.

Ideas: give examples of homotopy equivalent spaces, and spaces which "appear" not homotopy equivalent. Is homotopy equivalence an equivalence relation. Why is it hard to show two spaces are not homotopy equivalent? Is the 1 point space equivalent to the (discrete) 2 point space? Check out exercise 8.2.