quasiSober — Mathlib

English

A space is quasi-sober iff every member of a given open cover is quasi-sober, and a corresponding condition holds on overlaps.

Русский

Пространство квазисоберно тогда и только тогда, когда каждый элемент открытого покрытия квазисоберен.

LaTeX

$$$\\text{QuasiSober}(\\alpha) \\iff \\forall i, \\text{QuasiSober}(U_i).$$$

Lean4

theorem quasiSober {ι : Type*} {U : ι → Opens α} (hU : TopologicalSpace.IsOpenCover U) [∀ i, QuasiSober (U i)] :
    QuasiSober α :=
  hU.quasiSober_iff_forall.mpr ‹_›

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