Theorems · Theorem · functional analysis

Bornology.IsVonNBounded.image

∀ {E : Type u_3} {F : Type u_4} {𝕜₁ : Type u_6} {𝕜₂ : Type u_7} [inst : NormedDivisionRing 𝕜₁]
  [inst_1 : NormedDivisionRing 𝕜₂] [inst_2 : AddCommGroup E] [inst_3 : Module 𝕜₁ E] [inst_4 : AddCommGroup F]
  [inst_5 : Module 𝕜₂ F] [inst_6 : TopologicalSpace E] [inst_7 : TopologicalSpace F] {σ : 𝕜₁ →+* 𝕜₂}
  [RingHomSurjective σ] [RingHomIsometric σ] {s : Set E},
  Bornology.IsVonNBounded 𝕜₁ s → ∀ (f : E →SL[σ] F), Bornology.IsVonNBounded 𝕜₂ (⇑f '' s)

A continuous linear image of a bounded set is bounded.

Defined in

Mathlib.Analysis.LocallyConvex.Bounded

Cited by

5 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedDivisionRingNormedDivisionRingAddCommGroupModuleAddCommGroupModuleTopologicalSpaceTopologicalSpaceRingHomSurjectiveRingHomIsometric