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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

1. The interior \(B \setminus \delta B\) is open.
2. The closure \(B \cup \delta B\) is closed.
3. The closure \(B \cup \delta B\) is closed.

Table of Contents

Proofs: 1

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References

Bibliography

1. Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984