Definition:Topological Manifold with Boundary/Boundary Point

Definition

Let $M$ be a $n$-dimensional topological manifold with boundary.

Let $\partial \H^n$ denote the boundary of the closed upper half-space.

A point $p \in M$ is a boundary point of $M$ if and only if $p$ is in the domain of some boundary chart of $M$ that send $p$ to $\partial \H^n$.

Boundary

The boundary of $M$, denoted $\partial M$, is the set of all its boundary points.

Sources

• 2013: John M. Lee: Introduction to Smooth Manifolds (2nd ed.): Chapter $1$: Smooth Manifolds: $\S$ Manifolds with Boundary