Theorems · Theorem · functional analysis

ContinuousLinearMap.map_add

∀ {R₁ : Type u_1} {R₂ : Type u_2} [inst : Semiring R₁] [inst_1 : Semiring R₂] {σ₁₂ : R₁ →+* R₂} {M₁ : Type u_4}
  [inst_2 : TopologicalSpace M₁] [inst_3 : AddCommMonoid M₁] {M₂ : Type u_6} [inst_4 : TopologicalSpace M₂]
  [inst_5 : AddCommMonoid M₂] [inst_6 : Module R₁ M₁] [inst_7 : Module R₂ M₂] (f : M₁ →SL[σ₁₂] M₂) (x y : M₁),
  f (x + y) = f x + f y

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

16 results in Mathlib

Foundations

Depth 24 from the axioms · uses no axioms

Assumes

SemiringSemiringTopologicalSpaceAddCommMonoidTopologicalSpaceAddCommMonoidModuleModule