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Equicontinuous family of functions

A family

F

of maps between metric spaces is equicontinuous when, near each point, one input tolerance controls the output variation uniformly for every

f \in F

. Uniform equicontinuity uses one input tolerance over the whole domain.

Table of contents 130 3
- Arzela-Ascoli theorem Equicontinuous family of functions 92 2
  - Diagonal subsequence for locally uniform convergence Arzela-Ascoli theorem 62 1
    - Escaping bump counterexample to global uniform convergence Diagonal subsequence for locally uniform convergence 35

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