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?

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- Jun 14th 2011, 02:35 AMymara 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?

- Jun 14th 2011, 04:32 AMDevenoRe: a topology such that closed sets form a topology
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.

- Jun 14th 2011, 04:43 AMymarRe: a topology such that closed sets form a topology
Thank you, Deveno.