Theorems · Theorem · functional analysis

Bornology.IsVonNBounded.extend_scalars

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_6} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  (𝕝 : Type u_7) [inst_3 : NontriviallyNormedField 𝕝] [inst_4 : NormedAlgebra 𝕜 𝕝] [inst_5 : Module 𝕝 E]
  [inst_6 : TopologicalSpace E] [ContinuousSMul 𝕝 E] [IsScalarTower 𝕜 𝕝 E] {s : Set E},
  Bornology.IsVonNBounded 𝕜 s → Bornology.IsVonNBounded 𝕝 s

If a set is von Neumann bounded with respect to a smaller field, then it is also von Neumann bounded with respect to a larger field. See also Bornology.IsVonNBounded.restrict_scalars below.

Defined in

Mathlib.Analysis.LocallyConvex.Bounded

Cited by

2 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleNontriviallyNormedFieldNormedAlgebraModuleTopologicalSpaceContinuousSMulIsScalarTower