---
tag: 0M4JJT780X
kind: concept
name: Uniform continuity
msc: [26A15]
sources:
  - url: https://en.wikipedia.org/wiki/Uniform_continuity
    locator: lead section
same_as:
  wikidata: Q741865
  wikipedia: Uniform continuity
---

## Summary

A function is uniformly continuous when one input tolerance $\delta$ controls the output error $\varepsilon$ at all points of the domain at once. This is stronger than continuity at each point. The node [[uniform continuity|0Q4DR37DVE]] gives the precise definition.