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Math Help - a topology such that closed sets form a topology

  1. #1
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    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?
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  2. #2
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    Re: 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.
    Last edited by Deveno; June 14th 2011 at 05:45 AM.
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    Re: a topology such that closed sets form a topology

    Thank you, Deveno.
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