A function \(f:(a, b) \rightarrow \mathbb{R}\) is uniformly continuous if and only if \(f\) can be extended to a continuous function \(\tilde{f}:[a, b] \rightarrow \mathbb{R}\) (that is, there is a co...A function \(f:(a, b) \rightarrow \mathbb{R}\) is uniformly continuous if and only if \(f\) can be extended to a continuous function \(\tilde{f}:[a, b] \rightarrow \mathbb{R}\) (that is, there is a continuous function \(\tilde{f}:[a, b] \rightarrow \mathbb{R}\) such that \(f=\tilde{f}_{\mid(a, b)}\)).