---
tag: 0WQ19TJV24
kind: concept
name: Distance from a point to a set
msc: ["54E35"]
sources:
  - url: https://en.wikipedia.org/wiki/Hausdorff_distance
    locator: Definition
---

## Summary

In a metric space, the distance from a point $x$ to a nonempty set $A$ is the infimum of the distances $d(x, a)$ with $a \in A$.