Theorems · Theorem · general topology
Filter.comap_principal
∀ {α : Type u_1} {β : Type u_2} {m : α → β} {t : Set β},
Filter.comap m (Filter.principal t) = Filter.principal (m ⁻¹' t)- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 8,121
- Set.preimagestatement and proof · cited by 4,946
- LE.le.transproof · cited by 3,151
- Filter.principalstatement and proof · cited by 740
- Filter.comapstatement and proof · cited by 546
- Set.Subset.rflproof · cited by 255
- Set.preimage_monoproof · cited by 95
- Filter.extproof · cited by 60
Cited by47
Results whose statement or proof uses this declaration.
- IsProperMap.isCompact_preimageproof · cited by 12
- Filter.prod_principal_principalproof · cited by 9
- OrderIso.comap_atTopproof · cited by 6
- uniformContinuous_of_constproof · cited by 4
- Filter.comap_lift'_eqproof · cited by 4
- Filter.comap_pureproof · cited by 3
- IsUniformEmbedding.discreteUniformityproof · cited by 3
- AbsolutelyContinuousOnInterval.uniformContinuousOnproof · cited by 2
- TendstoUniformlyOn.compproof · cited by 2
- ultrafilter_comap_pure_nhdsproof · cited by 2
- UniformOnFun.uniformity_eq_of_basisproof · cited by 2
- Topology.IsOpenEmbedding.accPt_comap_iffproof · cited by 2