thumb|160px|Immersed manifold straight line with self-intersections In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S \rightarrow M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.
thumb|160px|Immersed manifold straight line with self-intersections In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S \rightarrow 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==
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).