Theorems · Theorem · general topology
Filter.comap_iInf
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_5} {m : α → β} {f : ι → Filter β},
Filter.comap m (⨅ i, f i) = ⨅ i, Filter.comap m (f i)- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 23 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- iInfstatement · cited by 1,690
- Filter.comapstatement · cited by 546
- GaloisConnection.u_iInfproof · cited by 40
- Filter.gc_map_comapproof · cited by 12
Cited by23
Results whose statement or proof uses this declaration.
- UniformSpace.comap_iInfproof · cited by 9
- UniformSpace.toTopologicalSpace_iInfproof · cited by 6
- OrderIso.comap_atTopproof · cited by 6
- LinearMap.withSeminorms_inducedproof · cited by 5
- Equicontinuous.comap_uniformFun_eqproof · cited by 3
- UniformConvergenceCLM.nhds_zero_eq_of_basisproof · cited by 2
- induced_topology_eq_preorderproof · cited by 2
- ultrafilter_comap_pure_nhdsproof · cited by 2
- UniformOnFun.uniformity_eq_of_basisproof · cited by 2
- UniformOnFun.isUniformEmbedding_toFun_finiteproof · cited by 2
- UniformOnFun.nhds_eq_of_basisproof · cited by 2
- comap_abs_nhds_zeroproof · cited by 1