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Proposition: How the Boundary Changes the Property of a Set of Being Open
Let \((X,\mathcal O)\) be a topological space and let \(B\subset X\). Then
 The interior \(B \setminus \delta B\) is open.
 The closure \(B \cup \delta B\) is closed.
 The closure \(B \cup \delta B\) is closed.
Table of Contents
Proofs: 1
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References
Bibliography
 Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984