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Ok, so a manifold is simply a hypersurface. At least I‘m pretty sure in machine learning it means exactly that.

A hypersurface is usually a codimension one object, while a manifold can have bigger codimension or even not be embedded in an higher dimensional space at all

Ok, a line in 3D space can also be called a manifold? Maybe a better question is then to ask, what is not a manifold?

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