---
tag: 0M85DXB5RM
kind: concept
name: Equivalent norms
aliases: [equivalence-of-norms]
msc: [46B20]
sources:
  - url: https://en.wikipedia.org/wiki/Norm_(mathematics)
    locator: Equivalence
---

## Summary

Two norms on a vector space are equivalent when each is bounded by a constant multiple of the other.
Equivalent norms give the same open sets, the same convergent sequences and the same Cauchy sequences.