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Theorems · Theorem · functional analysis

Bornology.IsVonNBounded.of_neg

∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : AddGroup E] [inst_2 : TopologicalSpace E]
  [IsTopologicalAddGroup E] [inst_4 : DistribMulAction 𝕜 E] {s : Set E},
  Bornology.IsVonNBounded 𝕜 (-s) → Bornology.IsVonNBounded 𝕜 s

Alias of the forward direction of Bornology.isVonNBounded_neg.

Defined in
Mathlib.Analysis.LocallyConvex.Bounded
Cited by
1 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedRingAddGroupTopologicalSpaceIsTopologicalAddGroupDistribMulAction
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Bornology.IsVonNBounded.of_sub_right · cited by 0IsVonNBounded.of_sub_rightSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceAddGroup · cited by 4410AddGroupIsTopologicalAddGroup · cited by 1394IsTopologicalAddGroupDistribMulAction · cited by 584DistribMulActionSeminormedRing · cited by 446SeminormedRingSet.neg · cited by 168Set.negBornology.IsVonNBounded · cited by 136Bornology.IsVonNBoundedBornology.isVonNBounded_neg · cited by 1Bornology.isVonNBounded_n…IsVonNBounded.of_negCITED BYCITES

Cites9

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.