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Two metric spaces (X,dx) and (Y,dY) are said to be bi-Lipshitz equivalent if there exists a...

Two metric spaces (X,dx) and (Y,dY) are said to be bi-Lipshitz equivalent if there exists a surjective function f: X -> Y and a number K >= 1 such that for all x1,x2 in X it the case (1/K)dx(x1,x2)<=dY(f(x1),f(x2))<=Kdx(x1,x2)

Prove the function f of the definition of bi-Lipschitz equivalence is a bijection. (Geometric group theory)

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