Theorems · Theorem · general topology
IsClosed.measurableSet_image_of_continuousOn_injOn
∀ {γ : Type u_3} [inst : TopologicalSpace γ] [PolishSpace γ] {β : Type u_4} [inst_2 : TopologicalSpace β] [T2Space β]
[inst_4 : MeasurableSpace β] [OpensMeasurableSpace β] {s : Set γ},
IsClosed s → ∀ {f : γ → β}, ContinuousOn f s → Set.InjOn f s → MeasurableSet (f '' s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- MeasurableSpacestatement and proof · cited by 13,106
- Set.Elemproof · cited by 7,166
- Set.imagestatement · cited by 5,609
- MeasurableSetstatement and proof · cited by 3,075
- IsClosedstatement and proof · cited by 1,639
- ContinuousOnstatement and proof · cited by 1,411
- T2Spacestatement and proof · cited by 1,351
- OpensMeasurableSpacestatement and proof · cited by 636
- Set.InjOnstatement and proof · cited by 543
- PolishSpacestatement and proof · cited by 57
Cited by1
Results whose statement or proof uses this declaration.
- MeasurableSet.image_of_continuousOn_injOnproof · cited by 6