Theorems · Theorem · functional analysis

ContinuousLinearMap.comp_apply

∀ {R₁ : Type u_1} {R₂ : Type u_2} {R₃ : Type u_3} [inst : Semiring R₁] [inst_1 : Semiring R₂] [inst_2 : Semiring R₃]
  {σ₁₂ : R₁ →+* R₂} {σ₂₃ : R₂ →+* R₃} {σ₁₃ : R₁ →+* R₃} {M₁ : Type u_4} [inst_3 : TopologicalSpace M₁]
  [inst_4 : AddCommMonoid M₁] {M₂ : Type u_6} [inst_5 : TopologicalSpace M₂] [inst_6 : AddCommMonoid M₂] {M₃ : Type u_7}
  [inst_7 : TopologicalSpace M₃] [inst_8 : AddCommMonoid M₃] [inst_9 : Module R₁ M₁] [inst_10 : Module R₂ M₂]
  [inst_11 : Module R₃ M₃] [inst_12 : RingHomCompTriple σ₁₂ σ₂₃ σ₁₃] (g : M₂ →SL[σ₂₃] M₃) (f : M₁ →SL[σ₁₂] M₂) (x : M₁),
  (g ∘SL f) x = g (f x)

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

13 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringSemiringTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModuleModuleRingHomCompTriple