About: 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 be a manifold with boundary, and be a submanifold of . 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.