Theorems · Theorem · general topology
IsDiscrete.image_of_isOpenMap_of_isOpen
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set X},
IsDiscrete s → IsOpenMap f → IsOpen s → IsDiscrete (f '' s)- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- TopologicalSpacestatement and proof · cited by 24,529
- Filterproof · cited by 8,121
- Set.imagestatement and proof · cited by 5,609
- nhdsproof · cited by 5,554
- IsOpenstatement and proof · cited by 2,400
- Filter.mapproof · cited by 819
- IsOpenMapstatement and proof · cited by 253
- IsDiscretestatement and proof · cited by 86
- IsOpen.nhdsWithin_eqproof · cited by 15
- IsOpenMap.nhds_leproof · cited by 11
- Filter.map_pureproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- IsOpenMap.isDiscrete_rangeproof · cited by 0