Theorems · Theorem · general topology
Filter.HasBasis.smallSets
∀ {α : Type u_1} {ι : Sort u_3} {l : Filter α} {p : ι → Prop} {s : ι → Set α},
l.HasBasis p s → l.smallSets.HasBasis p fun i => 𝒫 s i- Defined in
- Mathlib.Order.Filter.SmallSets
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.smallSetsstatement · cited by 89
- Set.powersetstatement · cited by 67
- Filter.HasBasis.lift'proof · cited by 8
- Set.monotone_powersetproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- VitaliFamily.tendsto_filterAt_iffproof · cited by 5
- Filter.hasBasis_smallSetsproof · cited by 2
- Filter.Eventually.exists_mem_basis_of_smallSetsproof · cited by 1
- Filter.HasBasis.vitaliFamilyproof · cited by 1
- ContDiffBump.tendsto_support_normed_smallSetsproof · cited by 1
- iteratedFDerivWithin_comp_of_eventually_memproof · cited by 1
- LocallyFinite.exists_mem_basisproof · cited by 0
- Filter.HasBasis.tendstoIxxClassproof · cited by 0
- Filter.Frequently.smallSets_of_forall_mem_basisproof · cited by 0