# Continuous image of a compact set

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)



## [Continuous image of a compact set](https://ocme.evemisslab.com/en/atlas/atlas-continuous-image-of-compact/)

If K is compact in X and f:X→Y is continuous, then f(K) is compact in Y.

atlas-continuous-image-of-compact · canonical_mko

[Continuous image of a compact set](https://ocme.evemisslab.com/en/mko/mko-continuous-image-of-compact/)

## Prerequisite nodes


- [Compact subset](https://ocme.evemisslab.com/en/atlas/atlas-compact-subset/)
- [Continuous maps between topological spaces](https://ocme.evemisslab.com/en/atlas/atlas-topological-continuity/)
- [Function mapping](https://ocme.evemisslab.com/en/atlas/atlas-function-mapping/)