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Proposition: Metric Spaces and Empty Sets are Clopen
Every metric space \((X,d)\) and the empty set \(\emptyset\) are both, open and closed (i.e. they are clopen).
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- Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984