Theorems · Definition · functional analysis

ContinuousLinearEquiv.prodComm

(R₁ : Type u_1) →
  [inst : Semiring R₁] →
    (M₁ : Type u_4) →
      [inst_1 : TopologicalSpace M₁] →
        [inst_2 : AddCommMonoid M₁] →
          (M₂ : Type u_5) →
            [inst_3 : TopologicalSpace M₂] →
              [inst_4 : AddCommMonoid M₂] → [inst_5 : Module R₁ M₁] → [inst_6 : Module R₁ M₂] → (M₁ × M₂) ≃L[R₁] M₂ × M₁

Product of topological modules is commutative up to continuous linear isomorphism.

Defined in

Mathlib.Topology.Algebra.Module.Equiv

Cited by

7 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModule