> A family of sets gives rise naturally to a lattice. A lattice gives
> rise naturally to a poset. A poset gives rise naturally to a
> topological space. But a topological space is just a certain type of
> set family, and thus set families generalize topological spaces.

> All these generalizations are proper: not every lattice would induce a
> set family, nor would every poset induce a lattice, nor would every
> topological space induce a poset (only the T0 spaces).

> Thus set families are a proper generalization of set families.