(related to Corollary: Closed Real Intervals Are Compact)

- According to the respective proposition, closed $n$-dimensional cuboids of \(\mathbb R^n\) are compact.
- A closed real interval $[a,b]\subset\mathbb R$ is a special case of an $n$-dimensional closed cuboid for \(n=1\).
- Thus, it follows from the general case that it is a compact subset of the metric space of real numbers \(\mathbb R\).∎

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