Theorems · Theorem · functional analysis

WithSeminorms.isVonNBounded_iff_seminorm_bddAbove

∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NontriviallyNormedField 𝕜] [inst_1 : AddCommGroup E]
  [inst_2 : Module 𝕜 E] {p : SeminormFamily 𝕜 E ι} [inst_3 : TopologicalSpace E] {s : Set E},
  WithSeminorms p → (Bornology.IsVonNBounded 𝕜 s ↔ ∀ (i : ι), BddAbove (⇑(p i) '' s))

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

1 results in Mathlib

Foundations

Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldAddCommGroupModuleTopologicalSpace