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1:22:31

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: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.

### GeneralÂ