Theorems · Theorem · general topology
boundedSpace_induced_iff
∀ {α : Type u_5} {β : Type u_6} [inst : Bornology β] {f : α → β}, BoundedSpace α ↔ Bornology.IsBounded (Set.range f)- Defined in
- Mathlib.Topology.Bornology.Constructions
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Bornology
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.
- Setproof · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- Set.image_univproof · cited by 322
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- BoundedSpacestatement · cited by 26
- Bornology.isBounded_univproof · cited by 5
- Bornology.inducedstatement · cited by 5
- Bornology.isBounded_inducedproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- boundedSpace_subtype_iffproof · cited by 2