Neat submanifold

In differential topology, an area of mathematics, a neat submanifold of a manifold with boundary is a kind of "well-behaved" submanifold. More precisely, let be a manifold with boundary, and a submanifold of . A is said to be a neat submanifold of if it meets the following two conditions:[1]

  • The boundary of the submanifold is a subset of the boundary of the larger manifold. That is, .
  • Each point of the submanifold has a neighborhood within which the submanifold's embedding is equivalent to the embedding of a hyperplane in a higher-dimensional Euclidean space. More formally, must be covered by charts of such that where is the dimension of . For instance, in the category of smooth manifolds, this means that the embedding of must also be smooth.

See also

References

  1. Lee, Kotik K. (1992), Lectures on Dynamical Systems, Structural Stability, and Their Applications, World Scientific, p. 109, ISBN 9789971509651.


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