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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