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Question: 7 let e be a nonempty subset of a metric...

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(7) Let E be a nonempty subset of a metric space (X, d). Define the distance of a point x X to E by (a) Prove that ρ : X R is well-defined, i.e. the infimum exists for all x E X. (b) Prove that f(x) d(z, y) +a(y), for all x, y є x. (c) Prove that ρ is uniformly continuous on X.

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