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Theorems · Theorem · general topology

Bornology.forall_isBounded_image_eval_iff

∀ {ι : Type u_3} {X : ι → Type u_4} [inst : (i : ι) → Bornology (X i)] {s : Set ((i : ι) → X i)},
  (∀ (i : ι), Bornology.IsBounded (Function.eval i '' s)) ↔ Bornology.IsBounded s
Defined in
Mathlib.Topology.Bornology.Constructions
Cited by
3 results in Mathlib
Foundations
Depth 74 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_pi_of_nonempty · cited by 1Bornology.isBounded_pi_of…Bornology.IsBounded.pi · cited by 1IsBounded.piBornology.IsBounded.image_eval · cited by 0IsBounded.image_evalSet · cited by 53352SetSet.image · cited by 5609Set.imageBornology.IsBounded · cited by 293Bornology.IsBoundedBornology · cited by 188BornologyFunction.eval · cited by 140Function.evalFilter.compl_mem_coprodᵢ · cited by 1Filter.compl_mem_coprodᵢBornology.forall_isBounded_im…CITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.