---
tag: 0VKD1TP7F3
kind: concept
name: Metric space
msc: ["54E35"]
sources:
  - url: https://en.wikipedia.org/wiki/Metric_space
    locator: lead section
same_as:
  wikidata: Q180953
  wikipedia: Metric space
---

## Summary

A metric space is a set with a distance function between its points.
The distance is zero only from a point to itself, it is symmetric, and it satisfies the triangle inequality.
Metric spaces are the setting for limits, continuity and completeness beyond the real line.