Uniform Convergence - Properties

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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