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Proposition: Closed n-Dimensional Cuboids Are Compact
Let \(a_\nu,b_\nu\in\mathbb R\) be real numbers with \(a_\nu \le b_\nu\) for \(\nu=1,\ldots,n\). The closed $n$-dimensional cuboid \[Q:=\{(x_1,\ldots,x_n)\in\mathbb R^n:\quad a_\nu \le x_\nu \le b_\nu\}\]
is a compact subset of the \(n\)-dimensional metric space of real numbers \(\mathbb R^n\).
Table of Contents
Proofs: 1 Corollaries: 1
Mentioned in:
Proofs: 1 2
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References
Bibliography
- Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984
