Theorems · Theorem · general topology
specializingMap_iff_stableUnderSpecialization_image_singleton
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
SpecializingMap f ↔ ∀ (x : X), StableUnderSpecialization (f '' closure {x})- Defined in
- Mathlib.Topology.Inseparable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement and proof · cited by 5,609
- closurestatement · cited by 1,254
- StableUnderSpecializationstatement and proof · cited by 32
- SpecializingMapstatement and proof · cited by 21
- Relation.fibration_iff_isLowerSet_image_Iicproof · cited by 4
- closure_singleton_eq_Iicproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsClosedMap.specializingMapproof · cited by 2
- specializingMap_iff_isClosed_image_closure_singletonproof · cited by 0