Theorems · Theorem · functional analysis

withSeminorms_pi

∀ {𝕜 : Type u_2} {ι : Type u_9} [inst : NormedField 𝕜] {κ : ι → Type u_11} {E : ι → Type u_12}
  [inst_1 : (i : ι) → AddCommGroup (E i)] [inst_2 : (i : ι) → Module 𝕜 (E i)]
  [inst_3 : (i : ι) → TopologicalSpace (E i)] {p : (i : ι) → SeminormFamily 𝕜 (E i) (κ i)},
  (∀ (i : ι), WithSeminorms (p i)) → WithSeminorms (SeminormFamily.sigma fun i => (p i).comp (LinearMap.proj i))

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

3 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleTopologicalSpace