Submanifold: Difference between revisions

197 bytes added ,  4 years ago
Added another reference for topological submanifolds.
(Added note about the difference between embedded and regular topological submanifolds.)
(Added another reference for topological submanifolds.)
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 ''C''<sup>''r''</sup> submanifolds with ''r'' = 0.<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.
* {{cite book|ref=harv|last=Choquet-Bruhat|first=Yvonne|title=Géométrie différentielle et systèmes extérieurs|publisher=Dunod|location=Paris|year=1968}}
*{{cite book|ref=harv|last=Kosinski|first=Antoni Albert|year=2007|origyear=1993|title=Differential manifolds|location=Mineola, New York|publisher=Dover Publications|isbn=978-0-486-46244-8}}
*{{Cite book|ref=harv | isbn = 978-0-387-98593-0 | title = Fundamentals of Differential Geometry | last1 = Lang | first1 = Serge |authorlink1=Serge Lang| year = 1999 | series = Graduate Texts in Mathematics}}