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In mathematics, particularly in topology, a topological space X is sober if every irreducible closed subset of X is the closure of exactly one singleton of X.
An irreducible closed subset of X is defined to be a nonempty closed subset of X which is not the union of two proper closed subsets of itself.
Any Hausdorff (<math>T_2<math>) space is sober, and all
sober spaces are Kolmogorov (<math>T_0<math>). Sobriety is
not comparable to NaodW29-math2f973eb65266513d00000003.
Sobriety of X is precisely the condition that forces the lattice of open subsets of X to determine X up to homeomorphism.
Sobriety makes the specialization preorder
a DCPO.
See also pointless topology.
External link
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Example Usage of Sober |
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tay_hitmebaby: They're pissy drunk over here, and I'm Sober as a door knob : / ....NOT FOR LONGGGG! |
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ms_mayo: @ahndreeuh we have fun when were Sober 2 we just dont have stuff 2 do right now.were not alcoholics lyk ur makin it seem |
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Popher: Had a decaff latte and much flat time - Sober though. Surprisingly late. Shall get some rest. |
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