Submanifold: Difference between revisions

1 byte removed ,  10 years ago
(→‎Immersed submanifolds: need not be one-to-one)
===Immersed submanifolds===
[[Image:immersedsubmanifold_nonselfintersectionimmersedsubmanifold nonselfintersection.jpg|thumb|150px|Immersed submanifold open interval with interval ends mapped to arrow marked ends.]]
An '''immersed submanifold''' of a manifold ''M'' is the image ''S'' of an [[immersion (mathematics)|immersion]] map ''i'': ''N'' → ''M''; in general this image will not be a submanifold as a subset, and an immersion map need not even be one-to-one – it can have self-intersections – so the term is used loosely.
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