Submanifold: Difference between revisions

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Deleted 'fortunately' - see Wikipedia:Manual_of_Style/Words_to_watch#Editorializing - and a superfluous 'actually'.
m (Deleted 'fortunately' - see Wikipedia:Manual_of_Style/Words_to_watch#Editorializing - and a superfluous 'actually'.)
==Submanifolds of real coordinate space==
 
Smooth manifolds are sometimes ''defined'' as embedded submanifolds of [[real coordinate space]] '''R'''<sup>''n''</sup>, for some ''n''. Fortunately, thisThis point of view is actually equivalent to the usual, abstract approach, because, by the [[Whitney embedding theorem]], any [[second-countable space|second-countable]] smooth (abstract) ''m''-manifold can be smoothly embedded in '''R'''<sup>2''m''</sup>.
 
==Notes==