---
tag: 05D5EGMFYV
kind: concept
name: Boundary
aliases: [frontier, boundary-of-a-set]
msc: [54A05]
sources:
  - url: https://en.wikipedia.org/wiki/Boundary_(topology)
    locator: lead section
same_as:
  wikidata: Q875399
  wikipedia: Boundary (topology)
---

## Summary

The boundary of a subset of a topological space is the set of points in its closure that are not in its interior.
Each neighbourhood of a boundary point meets both the subset and its complement.