# A uniform limit of continuous functions is continuous

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [A uniform limit of continuous functions is continuous](https://ocme.evemisslab.com/en/atlas/atlas-uniform-limit-continuity-theorem/)

Continuous functions on one common domain have a continuous limit when convergence is uniform on that domain.

atlas-uniform-limit-continuity-theorem · canonical_mko

[A uniform limit of continuous functions is continuous](https://ocme.evemisslab.com/en/mko/mko-uniform-limit-continuity-theorem/)

## Prerequisite nodes


- [Uniform convergence of functions](https://ocme.evemisslab.com/en/atlas/atlas-uniform-convergence-of-functions/)
- [Point values and continuity of real functions](https://ocme.evemisslab.com/en/atlas/atlas-continuity/)
- [Function mapping](https://ocme.evemisslab.com/en/atlas/atlas-function-mapping/)
- [Supremum and infimum](https://ocme.evemisslab.com/en/atlas/atlas-supremum-and-infimum/)