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Theorems · Theorem · general topology

Filter.HasBasis.ker

∀ {α : Type u_1} {ι : Sort u_4} {l : Filter α} {p : ι → Prop} {s : ι → Set α},
  l.HasBasis p s → l.ker = ⋂ i, ⋂ (_ : p i), s i
Defined in
Mathlib.Order.Filter.Bases.Basic
Cited by
4 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

nhdsKer_def · cited by 4nhdsKer_defbiInter_basis_nhds · cited by 2biInter_basis_nhdsFilter.countable_compl_ker · cited by 1Filter.countable_compl_kerCircle.eq_one_of_forall_pow_mem_centeredArc_pi_div_two · cited by 0Circle.eq_one_of_forall_p…Set · cited by 53352SetFilter · cited by 8121FilterSet.iInter · cited by 1084Set.iInterFilter.HasBasis · cited by 604Filter.HasBasisFilter.ker · cited by 40Filter.kermonotone_id · cited by 31monotone_idSet.sInter_eq_biInter · cited by 23Set.sInter_eq_biInterFilter.HasBasis.biInter_mem · cited by 2HasBasis.biInter_memHasBasis.kerCITED BYCITES

Cites8

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Cited by4

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