Theorems · Theorem · functional analysis

Topology.IsInducing.polynormableSpace

∀ {𝕜 : Type u_2} {𝕜₂ : Type u_3} {E : Type u_6} {F : Type u_7} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : NormedField 𝕜₂] [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂}
  [RingHomIsometric σ₁₂] [inst_7 : TopologicalSpace F] [PolynormableSpace 𝕜₂ F] [inst_9 : TopologicalSpace E]
  {f : E →ₛₗ[σ₁₂] F}, Topology.IsInducing ⇑f → PolynormableSpace 𝕜 E

Defined in

Mathlib.Analysis.LocallyConvex.WithSeminorms

Cited by

0 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleNormedFieldAddCommGroupModuleRingHomIsometricTopologicalSpacePolynormableSpaceTopologicalSpace