Submanifold: Difference between revisions
→Immersed submanifolds
(→top: ce) 

An '''immersed submanifold''' of a manifold ''M'' is the image ''S'' of an [[immersion (mathematics)immersion]] map ''f'': ''N'' → ''M''; in general this image will not be a submanifold as a subset, and an immersion map need not even be [[injective]] (onetoone) – it can have selfintersections.<ref>{{harvnbSharpe1997page=26}}.</ref>
More narrowly, one can require that the map ''f'': ''N'' → ''M'' be an
Given any injective immersion ''f'' : ''N'' → ''M'' the [[image (mathematics)image]] of ''N'' in ''M'' can be uniquely given the structure of an immersed submanifold so that ''f'' : ''N'' → ''f''(''N'') is a [[diffeomorphism]]. It follows that immersed submanifolds are precisely the images of injective immersions.
