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weak contraction

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Let M be a subset of a metric space (X,d). A function f: M -----> M is a weak contraction provided that for any x not equal to y in M, d ( f(x), f (y) ) < d ( x, y).

a) Is a weak contraction a contraction? ( Proof or counterexample)

b) If M is compact. Is a weak contraction a contraction? ( Proof or counterexample)

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Extreme Value Theorem is clearly integrated.

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