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(a) If G is an open set and K is a compact set with K ⊆...

(a) If G is an open set and K is a compact set with K ⊆ G, show that there exists a δ > 0 such that {x|dist(x, K) < δ} ⊆ G.

(b) Find an example of an open subset G in a metric space X and a closed, non compact subset F of G such that there is no δ > 0 with {x|dist(x, F) < δ} ⊆ G

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