Theorems · Theorem · functional analysis
Bornology.IsVonNBounded.restrict_scalars
∀ (𝕜 : Type u_1) {𝕜' : Type u_2} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : NormedRing 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] [inst_3 : Zero E] [inst_4 : TopologicalSpace E] [inst_5 : SMul 𝕜 E]
[inst_6 : MulActionWithZero 𝕜' E] [IsScalarTower 𝕜 𝕜' E] {s : Set E},
Bornology.IsVonNBounded 𝕜' s → Bornology.IsVonNBounded 𝕜 s- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- TopologicalSpacestatement and proof · cited by 24,529
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialproof · cited by 2,416
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- NormedRingstatement and proof · cited by 924
- subsingleton_or_nontrivialproof · cited by 161
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- MulActionWithZerostatement and proof · cited by 79
- MulActionWithZero.subsingletonproof · cited by 3
- Bornology.IsVonNBounded.of_subsingletonproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.isUniformEmbedding_restrictScalarsproof · cited by 3
- ContinuousLinearMap.isUniformEmbedding_restrictScalarsproof · cited by 2