Theorems · Theorem · general topology
Filter.exists_antitone_basis
∀ {α : Type u_1} (f : Filter α) [f.IsCountablyGenerated], ∃ x, f.HasAntitoneBasis xA countably generated filter admits a basis formed by an antitone sequence of sets.
- Defined in
- Mathlib.Order.Filter.CountablyGenerated
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.IsCountablyGenerated
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- Filter.basis_setsproof · cited by 105
- Filter.HasAntitoneBasisstatement and proof · cited by 43
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- Filter.exists_seq_tendstoproof · cited by 21
- MeasureTheory.measurableSet_exists_tendstoproof · cited by 4
- measurableSet_tendstoproof · cited by 2
- Filter.exists_antitone_seqproof · cited by 2
- IsSeqCompact.isCompleteproof · cited by 1
- IsTopologicalAddGroup.exists_antitone_basis_nhds_zeroproof · cited by 1
- Filter.countable_compl_kerproof · cited by 1
- IsTopologicalGroup.exists_antitone_basis_nhds_oneproof · cited by 0
- Filter.isCountablyGenerated_iff_exists_antitone_basisproof · cited by 0
- UniformOnFun.isCountablyGenerated_uniformityproof · cited by 0