Examples
- Every Lipschitz continuous map between two metric spaces is uniformly continuous. In particular, every function which is differentiable and has bounded derivative is uniformly continuous. More generally, every Hölder continuous function is uniformly continuous.
- Every member of a uniformly equicontinuous set of functions is uniformly continuous.
- The tangent function is continuous on the interval (−π/2, π/2) but is not uniformly continuous on that interval.
- The exponential function x ex is continuous everywhere on the real line but is not uniformly continuous on the line.
Read more about this topic: Uniform Continuity
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