Theorems · Definition · functional analysis

WithLp.prodContinuousLinearEquiv

(p : ENNReal) →
  (𝕜 : Type u_1) →
    (α : Type u_2) →
      (β : Type u_3) →
        [inst : TopologicalSpace α] →
          [inst_1 : TopologicalSpace β] →
            [inst_2 : Semiring 𝕜] →
              [inst_3 : AddCommGroup α] →
                [inst_4 : AddCommGroup β] → [inst_5 : Module 𝕜 α] → [inst_6 : Module 𝕜 β] → WithLp p (α × β) ≃L[𝕜] α × β

WithLp.equiv as a continuous linear equivalence.

Defined in

Mathlib.Analysis.Normed.Lp.ProdLp

Cited by

15 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSemiringAddCommGroupAddCommGroupModuleModule