Theorems · Theorem · general topology
Filter.map_pure
∀ {α : Type u_1} {β : Type u_2} (f : α → β) (a : α), Filter.map f (pure a) = pure (f a)- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement · cited by 8,121
- Filter.mapstatement · cited by 819
Cited by9
Results whose statement or proof uses this declaration.
- Filter.pure_prodproof · cited by 10
- Specializes.map_of_continuousWithinAtproof · cited by 3
- IsDiscrete.preimageproof · cited by 1
- Subgroup.discreteTopology_iff_of_finiteIndexproof · cited by 1
- Filter.filter_injOn_Iic_iff_injOnproof · cited by 1
- IsDiscrete.image_of_isOpenMap_of_isOpenproof · cited by 1
- AddSubgroup.discreteTopology_iff_of_finiteIndexproof · cited by 1
- IsDiscrete.image_of_isOpenMapproof · cited by 0
- Filter.map₂_pureproof · cited by 0