Let y: [0,1] C be a closed path. Let p be the same path traversed in the opposite direction, i.e. 7 (t) = y(1 t). Let a be any point not on y. Given two closed paths 71, 72: [0, 1] C with 72 (0) = 71(1) their concatentation 1 * 72: [0, 2] C is defined as 71 * 72 (t) = In(t) for t = [0, 1] [2(t-1) for t [1, 2] = Let UC C be open and let y: [0, 1] U be a closed path. Prove that yop is homotopic to a constant path rel end points. Y