Submanifold: Difference between revisions
→Immersed submanifolds
[[Image:immersedsubmanifold nonselfintersection.jpgthumb150pxImmersed submanifold open interval with interval ends mapped to arrow marked ends]]
An '''immersed
More narrowly, one can require that the map ''f'': ''N'' → ''M'' be an inclusion (onetoone), in which we call it an [[injective]] [[immersion (mathematics)immersion]], and define an '''immersed submanifold''' to be the image subset ''S'' together with a [[topology (structure)topology]] and [[differential structure]] such that ''S'' is a manifold and the inclusion ''f'' is a [[diffeomorphism]]: this is just the topology on ''N,'' which in general will not agree with the subset topology: in general the subset ''S'' is not a submanifold of ''M,'' in the subset topology.
