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A set E in a metric space is called clopen if it is both open and closed.

a) Prove that every metric space has at least two clopen sets.

b) Prove that a metric space is connected if and only if it contains exactly two clopen sets.

a) Prove that every metric space has at least two clopen sets.

b) Prove that a metric space is connected if and only if it contains exactly two clopen sets.

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