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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.

| | | | | created: 2017-03-13 12:39:54 | modified: 2017-03-13 12:42:52 | by: bookofproofs | references: [582]

## 1.Proof: (related to "Continuous Functions on Compact Domains are Uniformly Continuous")

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[582] Forster Otto: “Analysis 2, Differentialrechnung im $$\mathbb R^n$$, Gewöhnliche Differentialgleichungen”, Vieweg Studium, 1984