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Theorems · Theorem · general topology

Filter.HasBasis.eq_iInf

∀ {α : Type u_1} {ι : Sort u_4} {l : Filter α} {s : ι → Set α},
  l.HasBasis (fun x => True) s → l = ⨅ i, Filter.principal (s i)
Defined in
Mathlib.Order.Filter.Bases.Basic
Cited by
5 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.map_atTop_eq · cited by 1Filter.map_atTop_eqEReal.nhds_top' · cited by 0EReal.nhds_top'Filter.isCountablyGenerated_iff_exists_antitone_basis · cited by 0Filter.isCountablyGenerat…Filter.map_atBot_eq · cited by 0Filter.map_atBot_eqEReal.nhds_bot' · cited by 0EReal.nhds_bot'Set · cited by 53352SetFilter · cited by 8121FilteriInf · cited by 1690iInfFilter.principal · cited by 740Filter.principalFilter.HasBasis · cited by 604Filter.HasBasisFilter.HasBasis.eq_biInf · cited by 15HasBasis.eq_biInfiInf_true · cited by 3iInf_trueHasBasis.eq_iInfCITED BYCITES

Cites7

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Cited by5

Results whose statement or proof uses this declaration.