Manifold with boundary
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.
The term manifold with boundary is sometimes used not for the manifold itself, but for the pair comprising the manifold and its boundary (the set of its boundary points).