[Jared Davis wrote](https://forum.azimuthproject.org/discussion/comment/16828/#Comment_16828):

> Is the only difference between a partition and a topology that the empty set is not part of the partition and that the member sets of the partition are disjoint?

No, there are other differences. Check out [the definition of a topology](https://en.wikipedia.org/wiki/Topology#Topologies_on_sets). They're so different that I'd rather not talk about topology here.