---
tag: 06GZ956657
kind: concept
name: Banach space
aliases: [complete-normed-space]
msc: [46B99]
sources:
  - url: https://en.wikipedia.org/wiki/Banach_space
    locator: lead section
same_as:
  wikidata: Q194397
  wikipedia: Banach space
---

## Summary

A Banach space is a normed vector space that is complete for the metric of its norm.
Banach spaces are the main setting of functional analysis.