State and prove Proposition 1.33 (the lifting criterion). State and prove Proposition 1.34. Define what it means for a space to be semilocally simply-connected (p.63) and show why this condition is necessary for a space to have a simply-connected covering space (next time we show how to construct such a cover). Give the example in the last paragraph of p. 63 of a space that is not semilocally simply connected.
Note: In the last paragraph on p. 63, Hatcher talks about "locally simply connected" however, I cannot find any place where he defines this. For your knowlege, a space is locally simply connected at x if every neighborhood of x contains a simply connected neighborhood of x. A space X is locally simply connected if it is locally simply connected at every x in X. The notion of locally simply connected will not be important for our purposes so you do not need to talk about this.