Yes and no. The definition doesn't require that what you have is embedded in a higher dimensional space. Though that's a good source of examples. https://en.m.

Yes and no. The definition doesn't require that what you have is embedded in a higher dimensional space. Though that's a good source of examples. https://en.m.wikipedia.org/wiki/Whitney_embedding_theorem https://en.m.wikipedia.org/wiki/Whitney_embedding_theorem Basically says that many manifolds can be described as a lower dimensional submanifold of some euclidean space.