Theorems · Theorem · general topology
Filter.map_comap_of_mem
∀ {α : Type u_1} {β : Type u_2} {f : Filter β} {m : α → β}, Set.range m ∈ f → Filter.map m (Filter.comap m f) = f- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.rangestatement and proof · cited by 4,705
- Filter.mapstatement · cited by 819
- Filter.comapstatement · cited by 546
- Filter.le_principal_iffproof · cited by 87
- inf_eq_leftproof · cited by 41
- Filter.map_comapproof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- Filter.map_comap_of_surjectiveproof · cited by 11
- Filter.tendsto_comap'_iffproof · cited by 5
- map_nhds_induced_of_memproof · cited by 2
- map_coe_atTop_of_Ioo_subsetproof · cited by 2
- Filter.image_mem_of_mem_comapproof · cited by 1
- Filter.mem_comap_iffproof · cited by 1
- Equicontinuous.tendsto_uniformFun_iff_piproof · cited by 1
- inducing_sigmaproof · cited by 1
- Filter.comap_le_comap_iffproof · cited by 0