Theorems · Theorem · general topology
Filter.map_top
∀ {α : Type u_1} {β : Type u_2} (f : α → β), Filter.map f ⊤ = Filter.principal (Set.range f)- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Top.topstatement · cited by 9,680
- Filterstatement and proof · cited by 8,121
- Set.rangestatement and proof · cited by 4,705
- Filter.mapstatement and proof · cited by 819
- Filter.principalstatement and proof · cited by 740
- Set.image_univproof · cited by 322
- Filter.principal_univproof · cited by 46
- Filter.map_principalproof · cited by 17
Cited by6
Results whose statement or proof uses this declaration.
- Filter.principal_eq_map_coe_topproof · cited by 1
- Filter.limsup_top_eq_ciSupproof · cited by 1
- Filter.limsup_top_eq_iSupproof · cited by 1
- Filter.liminf_top_eq_ciInfproof · cited by 1
- Filter.liminf_top_eq_iInfproof · cited by 1
- Filter.map_inl_inf_map_inrproof · cited by 1