Thread: a topology such that closed sets form a topology

Is there a name for a topology such that the union of any family of closed sets is closed? Are those topologies exactly complete lattices, or am I talking nonsense?

i believe those are called alexandroff spaces. if i am not mistaken, such a topology can be used to define a pre-order in which the closed (or open) sets become a complete lattice.

Thank you, Deveno.