Show that for each n∈Z there is a unique function φ assigning an integer to each finite CW complex, such that (a) φ(X)=φ(Y) if X and Y are homeomorphic, (b) φ(X)=φ(A)+φ(X/A) if A is a subcomplex of X, and (c) φ(S0)=n. For such a function φ, show that φ(X)=φ(Y) if X≃Y.