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Theorem: Continuous Functions on Compact Domains are Uniformly Continuous

Let $(X,d_X)$ and $(Y,d_Y)$ be metric spaces. Let \(f:X\mapsto Y\) be a continuous function. If \(X\) is compact, then \(f:X\mapsto Y\) is uniformly continuous.

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Proofs: 1

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Proofs: 1

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References

Bibliography

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