---
tag: 07RB7B04HX
kind: concept
name: Uniform continuity on a set
msc: [26A15]
sources:
  - url: https://en.wikipedia.org/wiki/Uniform_continuity
    locator: Definition of uniform continuity
---

## Summary

A function is uniformly continuous on a set when its restriction to the set is uniformly continuous. Each continuous function on a closed bounded interval has this property. The node [[uniform continuity on a set|0A3CK6DVVB]] gives the precise definition.