[adamnemecek]

It can also just be some sort of partitioning. I would be really surprised if there was no partitioning of some space.

[mafribe]

Note that "some sort of partitioning" isn't a hyperplane. A partition is a set-theoretic concept. A hyperplane is (a generalisation of) a geometric concept, so has much more structure.

[adamnemecek]

Alright how about coalgebra.