  Suppose for closed surfaces $M,N$ there exists a continuous map $f:M\to N$ of
geometric degree $d>0$. Then $\chi(M)\le d\cdot\chi(N)$. This inequality was
first proved by Kneser in case of orientable surfaces and by Edmonds for
arbitrary $M,N$. We give a new simple proof of this result. Our proof is
completely elementary and does not use additional techniques (such as the
factorisation theorem of Edmonds and the absolute degree theory of Hopf).
