Theorems · Theorem · general topology
Bornology.IsBounded.prod
∀ {α : Type u_1} {β : Type u_2} [inst : Bornology α] [inst_1 : Bornology β] {s : Set α} {t : Set β},
Bornology.IsBounded s → Bornology.IsBounded t → Bornology.IsBounded (s ×ˢ t)- Defined in
- Mathlib.Topology.Bornology.Constructions
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 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 and proof · cited by 53,352
- SProd.sprodstatement · cited by 1,750
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- Bornology.IsBounded.subsetproof · cited by 45
- Set.fst_image_prod_subsetproof · cited by 5
- Set.snd_image_prod_subsetproof · cited by 5
- Bornology.isBounded_image_fst_and_sndproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Bornology.isBounded_prod_of_nonemptyproof · cited by 2
- Bornology.IsBounded.reProdImproof · cited by 1
- boundedSub_of_lipschitzWith_subproof · cited by 0