Manifold with boundary

Definition

A topological space is termed a manifold with boundary if it satisfies the following three conditions:

• It is a Hausdorff space.
• It is a second-countable space.
• It is a locally Euclidean half-space: every point has a neighborhood that is homeomorphic to an open subset of Euclidean half-space.

The points that have neighborhoods homeomorphic to open subsets of Euclidean space are termed interior points of the manifold; the other points are termed boundary points of the manifold.