Theorems · Theorem · functional analysis

ContinuousLinearMap.map_sub

∀ {R : Type u_1} [inst : Ring R] {R₂ : Type u_2} [inst_1 : Ring R₂] {M : Type u_4} [inst_2 : TopologicalSpace M]
  [inst_3 : AddCommGroup M] {M₂ : Type u_5} [inst_4 : TopologicalSpace M₂] [inst_5 : AddCommGroup M₂]
  [inst_6 : Module R M] [inst_7 : Module R₂ M₂] {σ₁₂ : R →+* R₂} (f : M →SL[σ₁₂] M₂) (x y : M), f (x - y) = f x - f y

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic

Cited by

10 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingRingTopologicalSpaceAddCommGroupTopologicalSpaceAddCommGroupModuleModule