Neat submanifold

In differential topology, an area of mathematics, a neat submanifold of a manifold with boundary is a kind of "well-behaved" submanifold.

To define this more precisely, first let

Then is said to be a neat submanifold of if it meets the following two conditions:

• The boundary of is a subset of the boundary of . That is, .
• Each point of has a neighborhood within which 's embedding in 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 For instance, in the category of smooth manifolds, this means that the embedding of must also be smooth.

See also

• Local flatness

References