Theorems · Theorem · general topology
Filter.map_principal
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {f : α → β}, Filter.map f (Filter.principal s) = Filter.principal (f '' s)- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, 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.
- Setstatement and proof · cited by 53,352
- Filterstatement · cited by 8,121
- Set.imagestatement · cited by 5,609
- Filter.mapstatement · cited by 819
- Filter.principalstatement · cited by 740
- Set.image_subset_iffproof · cited by 203
- Filter.extproof · cited by 60
Cited by17
Results whose statement or proof uses this declaration.
- Topology.IsInducing.isCompact_iffproof · cited by 9
- Filter.map_topproof · cited by 6
- Filter.comap_inf_principal_neBot_of_image_memproof · cited by 4
- Topology.IsInducing.isLindelof_iffproof · cited by 3
- isClosedMap_iff_clusterPtproof · cited by 1
- Topology.IsEmbedding.image_mem_codiscreteWithinproof · cited by 1
- Filter.map_surjOn_Iic_iff_surjOnproof · cited by 1
- Filter.map_lift'_eqproof · cited by 1
- Filter.smallSets_comap_eq_comap_imageproof · cited by 1
- hasFDerivWithinAt_comp_add_leftproof · cited by 1
- Topology.IsInducing.isCountablyCompact_iffproof · cited by 1
- Ultrafilter.ofComapInfPrincipal_eq_of_mapproof · cited by 0