I Am Looking To Prove That If U Is Compact And V Is Closed With Unv Intersection

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I am looking to prove that if U is compact and V is closed, with UnV (intersection) is empty, then d(U,V) > 0 (the distance between the sets).We define the distance between the sets as d(U,V) := {|x-y|:x in U, y in V}.Looking for help from someone comfortable in analysis/topology. 

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