Theorems · Theorem · general topology
Filter.image_mem_map
∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {m : α → β} {s : Set α}, s ∈ f → m '' s ∈ Filter.map m f- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.imagestatement · cited by 5,609
- Filter.mapstatement · cited by 819
- Set.subset_preimage_imageproof · cited by 44
- Filter.sets_of_supersetproof · cited by 14
Cited by39
Results whose statement or proof uses this declaration.
- Filter.prod_map_map_eqproof · cited by 17
- Filter.comap_mapproof · cited by 12
- IsOpenMap.of_nhds_leproof · cited by 10
- Filter.range_mem_mapproof · cited by 8
- Filter.push_pullproof · cited by 7
- Filter.mem_map_iff_exists_imageproof · cited by 6
- uniformContinuous_uniformly_extendproof · cited by 6
- Filter.map_infproof · cited by 5
- Real.dimH_of_mem_nhdsproof · cited by 3
- contMDiffWithinAt_iff_contMDiffOn_nhdsproof · cited by 3
- Filter.image_mem_map_iffproof · cited by 3
- GroupFilterBasis.nhds_eqproof · cited by 3