Question: A metric space (X, d) is called separable if it contains a countable dense subset, that is, if there exists a countable subset E Q

A metric space (X, d) is called separable if it contains a countable dense subset, that is, if there exists a countable subset E Q X such that E = X. Prove that every compact metric space is separable. Hint: For each n E N, consider an open cover consisting of neighborboods of radius 1 n '

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