Boundary of Manifold

Definition

Boundary Point of Manifold

Consider a Topological Manifold $(M,\mathcal{T})$. The point $x\in M$ is a boundary point if a Neighborhood ${\mathcal{N}}_x$ of the point $x$ is homeomorphic to the upper half space ${\mathbb{R}}_{+}^n$. $\exists {\mathcal{N}}_x\text{s.t.}{\mathcal{N}}_x\cong {\mathbb{R}}_{+}^n$

Boundary of Manifold

$\mathrm{Int}(M)$ The set of boundary points of the manifold $M$ is called an interior of $M$.