Theorems · Theorem · general topology
Bornology.IsBounded.image
∀ {F : Type u_1} {α : Type u_2} {β : Type u_3} [inst : FunLike F α β] [inst_1 : Bornology α] [inst_2 : Bornology β]
[LocallyBoundedMapClass F α β] (f : F) {s : Set α}, Bornology.IsBounded s → Bornology.IsBounded (⇑f '' s)- Defined in
- Mathlib.Topology.Bornology.Hom
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 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.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- FunLikestatement and proof · cited by 2,560
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- LocallyBoundedMapClassstatement and proof · cited by 2
- Bornology.comap_cobounded_le_iffproof · cited by 1
- LocallyBoundedMapClass.comap_cobounded_leproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- LipschitzWith.isBounded_imageproof · cited by 6
- InnerProductSpace.bounded_harmonic_on_complex_plane_is_constantproof · cited by 0