Properties
- Every uniformly convergent sequence is locally uniformly convergent.
- Every locally uniformly convergent sequence is compactly convergent.
- For locally compact spaces local uniform convergence and compact convergence coincide.
- A sequence of continuous functions on metric spaces, with the image metric space being complete, is uniformly convergent if and only if it is uniformly Cauchy.
Read more about this topic: Uniform Convergence
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