Definition 2-2 (simply connected space). Let M ⊆ ⊆ R n be non-empty and path-connected. M is called simply connected if and only if for any continuous loop, c : [0, 1] → M there exists a continuous tubular homotopy H : [0, 1] × [0, 1] → M from c to a fixed point p ∈ c ; that is,