If (M,d)  is a compact metric space and f:M→M  is an isometry (d(x,y)=d(f(x),f(y))  for any x,y∈M ), then f  is a homeomorphism.   I proved that $f$ is continuous as its inverse,I proved that it is injective also. I couldn't prove that it is also surjective...  thanks for any advance.
Possible Duplicate:          Let $X$ be a compact metric space and $f$ be an isometric map from $X$ to $X$. Prove $f$ is a surjective map.
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