# Real Banach 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)



## [Real Banach space](https://ocme.evemisslab.com/en/atlas/atlas-real-banach-space/)

A real normed vector space is a Banach space when it is complete in the metric induced by its own norm.

atlas-real-banach-space · canonical_mko

[Real Banach space](https://ocme.evemisslab.com/en/mko/mko-real-banach-space/)

## Prerequisite nodes


- [Real normed vector space](https://ocme.evemisslab.com/en/atlas/atlas-real-normed-vector-space/)
- [Norm-induced metric](https://ocme.evemisslab.com/en/atlas/atlas-norm-induced-metric/)
- [Complete metric space](https://ocme.evemisslab.com/en/atlas/atlas-complete-metric-space/)
- [Real vector space](https://ocme.evemisslab.com/en/atlas/atlas-real-vector-space/)