Theorems · Theorem · general topology
Filter.HasBasis.map
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} {l : Filter α} {p : ι → Prop} {s : ι → Set α} (f : α → β),
l.HasBasis p s → (Filter.map f l).HasBasis p fun i => f '' s i- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, 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
- Set.ofPredproof · cited by 6,101
- Set.imagestatement · cited by 5,609
- Filter.mapstatement · cited by 819
- Filter.HasBasisstatement and proof · cited by 604
- Filter.HasBasis.mem_iffproof · cited by 193
Cited by51
Results whose statement or proof uses this declaration.
- Filter.HasBasis.tendsto_left_iffproof · cited by 9
- Filter.HasBasis.map₂proof · cited by 6
- ModelWithCorners.locallyCompactSpaceproof · cited by 5
- ChartedSpace.locallyCompactSpaceproof · cited by 5
- Filter.limsup_eq_iInf_iSupproof · cited by 5
- Filter.limsup_eq_iInf_iSup_of_natproof · cited by 5
- Filter.HasBasis.limsup_eq_iInf_iSupproof · cited by 5
- Filter.map_atTop_eq_of_gc_preorderproof · cited by 3
- Filter.map_atTop_finsetProd_le_of_prod_eqproof · cited by 3
- Filter.map_atTop_finsetSum_le_of_sum_eqproof · cited by 3
- GroupFilterBasis.nhds_eqproof · cited by 3
- inv_atTop₀proof · cited by 3