Neat submanifold

• 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 For instance, in the category of smooth manifolds, this means that the embedding of must also be smooth.