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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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This work was contributed under CC BY-SA 3.0 by:

bookofproofs

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Bibliography (further reading)

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