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Definition: Diameter In Metric Spaces
Let \(A\) be a subset of a metric space $(X,d)$. The diameter $\operatorname{diam} (A)$ is defined as the supremum of all distances of any two points \(x,y\in A\), formally
\[\operatorname{diam} (A):=\sup\{d(x,y):~x,y\in A\}.\]
Mentioned in:
Proofs: 1 2 3
Theorems: 4
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References
Bibliography
- Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984
