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(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>{{harvnbKosinski2007page=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>{{harvnbLang1999pages=25–26}}. {{harvnbChoquetBruhat1968page=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.
==Properties==
==References==
* {{cite bookref=harvlast=ChoquetBruhatfirst=Yvonnetitle=Géométrie différentielle et systèmes extérieurspublisher=Dunodlocation=Parisyear=1968}}
*{{cite bookref=harvlast=Kosinskifirst=Antoni Albertyear=2007origyear=1993title=Differential manifoldslocation=Mineola, New Yorkpublisher=Dover Publicationsisbn=9780486462448}}
*{{Cite bookref=harv  isbn = 9780387985930  title = Fundamentals of Differential Geometry  last1 = Lang  first1 = Serge authorlink1=Serge Lang year = 1999  series = Graduate Texts in Mathematics}}
