---
tag: 7DS6B2BFK8
kind: concept
name: Manifold with boundary
msc: [57N99]
specializes: [0CQHFPGJ45]
sources:
  - url: https://en.wikipedia.org/wiki/Manifold
    locator: Manifold with boundary
---

## Summary

A manifold with boundary is a space that looks near each point either like $\R^n$ or like the closed half-space of $\R^n$.
The points of the second kind form the boundary, which is itself a manifold of dimension $n - 1$ without boundary.
Closed disks, closed intervals and solid balls are the first examples, and cobordism and surgery theory are built on them.

## Explanations

### L1 human

A closed disk is like a flat sheet with an edge.
Around a point inside, it looks like an open piece of the plane.
Around a point on the edge circle, it looks like a piece of a half-plane, with the edge as a border line.
The edge of the disk is the circle, and the circle has no edge of its own.
A closed interval $[0, 1]$ is a $1$-dimensional example whose boundary is the two end points.