Manifold with boundary: Difference between revisions
(New page: ==Definition== A topological space is termed a '''manifold with boundary''' if it satisfies the following three conditions: * It is a defining ingredient::Hausdorff space. * It is a ...) |
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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 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). | |||
Latest revision as of 00:43, 26 November 2008
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.
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).