TheoremBase

Continuity on a Closed Interval Implies Uniform Continuity

Statement

Let a,b∈Ra,b\in\mathbb{R} with a<ba<b. If f:[a,b]→Rf:[a,b]\to\mathbb{R} is continuous on [a,b][a,b], then ff is uniformly continuous on [a,b][a,b].

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