Question: Let E be a metric space. Let S E. Assume S is compact. Let f : E R be defined as f(x) = g.l.b.{d(x,s) :

Let E be a metric space. Let S E. Assume S is compact. Let f : E R be defined as f(x) = g.l.b.{d(x,s) : s S}.

1) Prove that, for all x E there exists u S such that f(x) = d(x,u).

2) Prove that f is continuous.

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