Answer to Question #15233 in Real Analysis for Michael Lauck

Question #15233

Let (M,d(x,y)) be a metric space and suppose that E, K are nonempty subsets of M with E closed, K compact, and E, K disjoint. Please show that there is a postive real number mu such that d(x,y) >= mu for every x contained in E and y contained in K, using either the definition of compactness in terms of open coverings or the limit point property.

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