Theorems · Theorem · general topology
Filter.map_le_iff_le_comap
∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {g : Filter β} {m : α → β}, Filter.map m f ≤ g ↔ f ≤ Filter.comap m g- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 19 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.preimageproof · cited by 4,946
- Filter.mapstatement and proof · cited by 819
- Filter.comapstatement and proof · cited by 546
- Filter.mem_of_supersetproof · cited by 308
- Set.Subset.rflproof · cited by 255
Cited by19
Results whose statement or proof uses this declaration.
- Filter.tendsto_comap_iffproof · cited by 55
- IsCompact.prodproof · cited by 26
- Filter.tendsto_iff_comapproof · cited by 19
- IsProperMap.isCompact_preimageproof · cited by 12
- Filter.gc_map_comapproof · cited by 12
- uniformContinuous_iff_le_comapproof · cited by 9
- uniformContinuous_of_constproof · cited by 4
- isInducing_stoneCechUnitproof · cited by 4
- Filter.map_le_map_iffproof · cited by 2
- UniformSpace.hausdorff.isUniformInducing_closureproof · cited by 2
- AddGroupFilterBasis.cauchy_iffproof · cited by 2
- IsDenseInducing.tendsto_comap_nhds_nhdsproof · cited by 2