Talk:Stone duality

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In the section The lattice of open sets I read that the lattice of open sets of a topological space is complete. I think this is not true in general, for the intersection of an arbitrary family of open sets need not be open. --fudo 12:17, 12 December 2006 (UTC)

  • OK, I think I got it. I'll write here my reasoning instead of deleting my previous comment so that it may help anybody else not to make the same mistake: Even if the intersection of an arbitrary family of open sets of a topological space need not be open, such a family DOES have an infimum in the open set lattice, which is the interior of its intersection. --fudo 12:48, 12 December 2006 (UTC)
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