Theorems · Theorem · functional analysis

ContinuousLinearMap.comp_toSpanSingleton

∀ {R₁ : Type u_1} [inst : Semiring R₁] {M₁ : Type u_4} [inst_1 : TopologicalSpace M₁] [inst_2 : AddCommMonoid M₁]
  {M₂ : Type u_6} [inst_3 : TopologicalSpace M₂] [inst_4 : AddCommMonoid M₂] [inst_5 : Module R₁ M₁]
  [inst_6 : Module R₁ M₂] [inst_7 : TopologicalSpace R₁] [inst_8 : ContinuousSMul R₁ M₂] [inst_9 : ContinuousSMul R₁ M₁]
  (f : M₁ →L[R₁] M₂) (x : M₁),
  f ∘SL ContinuousLinearMap.toSpanSingleton R₁ x = ContinuousLinearMap.toSpanSingleton R₁ (f x)

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModuleTopologicalSpaceContinuousSMulContinuousSMul