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:[1]
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.