Theorems · Theorem · general topology
Bornology.isBounded_biUnion_finset
∀ {ι : Type u_1} {α : Type u_2} [inst : Bornology α] (s : Finset ι) {f : ι → Set α},
Bornology.IsBounded (⋃ i ∈ s, f i) ↔ ∀ i ∈ s, Bornology.IsBounded (f i)- Defined in
- Mathlib.Topology.Bornology.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 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.
Cites7
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
- Finsetstatement and proof · cited by 13,712
- Set.iUnionstatement · cited by 2,483
- Bornology.IsBoundedstatement · cited by 293
- Finset.finite_toSetproof · cited by 210
- Bornologystatement and proof · cited by 188
- Bornology.isBounded_biUnionproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Bornology.isBounded_image_of_isLocallyBounded_of_isCompactproof · cited by 0