Topological Manifold - Manifolds With Boundary

Manifolds With Boundary

A slightly more general concept is sometimes useful. A topological manifold with boundary is a Hausdorff space in which every point has a neighborhood homeomorphic to an open subset of Euclidean half-space (for a fixed n):

The terminology is somewhat confusing: every topological manifold is a topological manifold with boundary, but not vice-versa.