Submanifold: Difference between revisions

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[[Image:immersedsubmanifold selfintersection.jpg|thumb|160px|Immersed manifold straight line with self-intersections]]
In [[mathematics]], a '''submanifoldsub''' of a [[manifold]] ''M'' is a [[subset]] ''S'' which itself has the structure of a manifold, and for which the [[inclusion map]] ''S'' → ''M'' satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.
==Formal definition==
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