# Path-connected space

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)



## [Path-connected space](https://ocme.evemisslab.com/en/atlas/atlas-path-connected-space/)

A space is path connected when every pair of its points is joined by a continuous map from the unit interval.

atlas-path-connected-space · canonical_mko

[Path-connected space](https://ocme.evemisslab.com/en/mko/mko-path-connected-space/)

## Prerequisite nodes


- [Continuous maps between topological spaces](https://ocme.evemisslab.com/en/atlas/atlas-topological-continuity/)
- [Connected topological space](https://ocme.evemisslab.com/en/atlas/atlas-connected-topological-space/)
- [Real number](https://ocme.evemisslab.com/en/atlas/atlas-real-number/)
- [Usual order on the real numbers](https://ocme.evemisslab.com/en/atlas/atlas-order-relation/)
- [Finite product topology](https://ocme.evemisslab.com/en/atlas/atlas-finite-product-topology/)
- [Intermediate value theorem](https://ocme.evemisslab.com/en/atlas/atlas-intermediate-value-theorem/)
- [Function composition](https://ocme.evemisslab.com/en/atlas/atlas-composition/)
- [Arithmetic operations](https://ocme.evemisslab.com/en/atlas/atlas-arithmetic-operations/)