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Let (X, d) be a compact metric space and F: X--> X be a function such...

Let (X, d) be a compact metric space and F: X--> X be a function such that d(F(x), F(y)) < d(x, y). Let G: X --> R be a function such that G(x) = d(F(x), x). Prove G is continuous (assume that it is proved that F is continuous).

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