Theorems · Theorem · general topology
Filter.HasBasis.ge_iff
∀ {α : Type u_1} {ι' : Sort u_5} {l l' : Filter α} {p' : ι' → Prop} {s' : ι' → Set α},
l'.HasBasis p' s' → (l ≤ l' ↔ ∀ (i' : ι'), p' i' → s' i' ∈ l)- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
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.HasBasisstatement and proof · cited by 604
- Filter.mem_of_supersetproof · cited by 308
- Filter.HasBasis.mem_iffproof · cited by 193
- Filter.HasBasis.mem_of_memproof · cited by 63
Cited by28
Results whose statement or proof uses this declaration.
- Filter.HasBasis.tendsto_right_iffproof · cited by 81
- Nat.cofinite_eq_atTopproof · cited by 37
- Filter.HasBasis.le_basis_iffproof · cited by 28
- Metric.cobounded_eq_cocompactproof · cited by 8
- specializes_TFAEproof · cited by 6
- TopologicalSpace.nhds_mkOfNhds_of_hasBasisproof · cited by 5
- Filter.HasBasis.lift'_closure_eq_selfproof · cited by 4
- Metric.cobounded_le_cocompactproof · cited by 4
- Filter.map_atTop_eq_of_gc_preorderproof · cited by 3
- Equicontinuous.comap_uniformFun_eqproof · cited by 3
- nhdsSet_diagonal_eq_uniformityproof · cited by 2
- Filter.map_atBot_eq_of_gc_preorderproof · cited by 2