Submanifold: Difference between revisions
→Embedded submanifolds
m (WP:CHECKWIKI error fixes (category with space) + general fixes using AWB (7796)) 

Given any [[embedding]] ''f'' : ''N'' → ''M'' of a manifold ''N'' in ''M'' the image ''f''(''N'') naturally has the structure of an embedded submanifold. That is, embedded submanifolds are precisely the images of embeddings.
There is an intrinsic definition of an embedded submanifold which is often useful. Let ''M'' be an ''n''dimensional manifold, and let ''k'' be an integer such that 0 ≤ ''k'' ≤ ''n''. A ''k''dimensional embedded submanifold of ''M'' is a
Alexander's theorem and jordanschoenflies are good examples of smooth embeddings.
