> > On Nov 5, 6:12 pm, taffer <djr...@bath.ac.uk> wrote:

> > > In what follows, everything (posets, lattices, topological spaces) is
> > > finite.

> > > 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.

> > In your first step, you say a family of
> > sets "gives rise naturally to a lattice."
> > But only certain families of sets (such
> > as a power set) are examples of lattices.
> > So your argument breaks down at its first
> > link.

> > regards, chip

> How could I be so stupid? But nevermind, skip that step; every set
> family gives rise to a poset. Every poset gives rise to a topological
> space, and every topological space gives rise to a set family. So we
> still have the set families generalize set families.

> What I'm wondering is, what is the right way to think about this?