Editing Submanifold (section)

===Other variations===

There are some other variations of submanifolds used in the literature. A [[neat submanifold]] is a manifold whose boundary agrees with the boundary of the entire manifold.<ref>{{harvnb|Kosinski|2007|page=27}}.</ref> Sharpe (1997) defines a type of submanifold which lies somewhere between an embedded submanifold and an immersed submanifold.

Many authors define topological submanifolds also. These are the same as <math>C^r</math> submanifolds with <math>r = 0</math>.<ref>{{harvnb|Lang|1999|pages=25–26}}. {{harvnb|Choquet-Bruhat|1968|page=11}}</ref> An embedded topological submanifold is not necessarily regular in the sense of the existence of a local chart at each point extending the embedding. Counterexamples include [[wild arc]]s and [[wild knot]]s.