Question: Let \(f: D \rightarrow \mathbb{R} .\) Mark each statement True or False. Justify each answer.

1. \(f\) is uniformly continuous on \(D\) iff for every \(\varepsilon>0\) there exists a \(\delta>0\) such that \(|f(x)-f(y)|<\delta\) whenever \(|x-y|<\varepsilon\) and \(x, y \in D\).
2. If \(D=\{x\}\), then \(f\) is uniformly continuous at \(x\).
3. If \(f\) is continuous and \(D\) is compact, then \(f\) is uniformly continuous on $D .$

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