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Theorems · Theorem · general topology

Bornology.isBounded_sUnion

∀ {α : Type u_2} [inst : Bornology α] {S : Set (Set α)},
  S.Finite → (Bornology.IsBounded (⋃₀ S) ↔ ∀ s ∈ S, Bornology.IsBounded s)
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
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Bornology.isBounded_iUnion · cited by 0Bornology.isBounded_iUnionSet · cited by 53352SetSet.Finite · cited by 1814Set.FiniteSet.sUnion · cited by 392Set.sUnionBornology.IsBounded · cited by 293Bornology.IsBoundedBornology · cited by 188BornologySet.sUnion_eq_biUnion · cited by 51Set.sUnion_eq_biUnionBornology.isBounded_biUnion · cited by 3Bornology.isBounded_biUni…Bornology.isBounded_sUnionCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.