# Pointwise convergence of functions

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)



## [Pointwise convergence of functions](https://ocme.evemisslab.com/en/atlas/atlas-pointwise-convergence-of-functions/)

A function sequence on one domain converges pointwise when its value sequence converges at each fixed x; the witness N may depend on x and epsilon.

atlas-pointwise-convergence-of-functions · canonical_mko

[Pointwise convergence of functions](https://ocme.evemisslab.com/en/mko/mko-pointwise-convergence-of-functions/)

## Prerequisite nodes


- [Sequence](https://ocme.evemisslab.com/en/atlas/atlas-sequence/)
- [Function mapping](https://ocme.evemisslab.com/en/atlas/atlas-function-mapping/)
- [Sequence limits and exact tail cutoffs](https://ocme.evemisslab.com/en/atlas/atlas-sequence-limit/)
- [Quantifiers and explicit domains](https://ocme.evemisslab.com/en/atlas/atlas-quantifier/)