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.
Read more about this topic: Topological Manifold
Famous quotes containing the word boundary:
“It appeared that he had once represented his tribe at Augusta, and also once at Washington, where he had met some Western chiefs. He had been consulted at Augusta, and gave advice, which he said was followed, respecting the eastern boundary of Maine, as determined by highlands and streams, at the time of the difficulties on that side. He was employed with the surveyors on the line. Also he called on Daniel Webster in Boston, at the time of his Bunker Hill oration.”
—Henry David Thoreau (1817–1862)