writes.casa

Let E be the set of all possible human interactions, and S_i a topology on it. S_i models the space of relations that an i-th society allows and classifies. Finally, let O be a partial order on E which corresponds to how humans would sort human interactions if they could observe and compare, without prejudice, every S_i, so that for any a and b of E, a > b would mean "a is preferable to b".

We call *alienating* an S_i that has no set containing the supremum of any given pair of point in the union of every element in S_i.

We call *alienated* a sequence in S_i that converges to a point M which is the supremum of all the other elements of the sequence, is in E, but not in S_i.

We call *longing* the supremum of an alienated sequence.

Exercise: from an alienated sequence of your choice, find an morphism from your current S_i to an S_j, that preserves O, but is not necessarily a homeomorphism from S_i to S_j, such as S_j contains your longing.