Theorems · Theorem · functional analysis

Seminorm.exists_le_comp_of_isInducing

∀ {𝕜₂ : Type u_3} {E : Type u_6} {F : Type u_7} [inst : AddCommGroup E] [inst_1 : NormedField 𝕜₂]
  [inst_2 : AddCommGroup F] [inst_3 : Module 𝕜₂ F] [inst_4 : TopologicalSpace F] {𝕜 : Type u_11}
  [inst_5 : NontriviallyNormedField 𝕜] [inst_6 : Module 𝕜 E] [inst_7 : TopologicalSpace E] {σ₁₂ : 𝕜 →+* 𝕜₂}
  [inst_8 : RingHomIsometric σ₁₂] {p : Seminorm 𝕜 E},
  Continuous ⇑p →
    ∀ [PolynormableSpace 𝕜₂ F] {f : E →ₛₗ[σ₁₂] F}, Topology.IsInducing ⇑f → ∃ p₂, Continuous ⇑p₂ ∧ p ≤ p₂.comp f

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

1 results in Mathlib

Foundations

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

Assumes

AddCommGroupNormedFieldAddCommGroupModuleTopologicalSpaceNontriviallyNormedFieldModuleTopologicalSpaceRingHomIsometricPolynormableSpace