Theorems · Theorem · geometry

ContinuousAffineMap.comp_contLinear

∀ {R : Type u_1} {V : Type u_2} {W : Type u_3} {P : Type u_4} {Q : Type u_5} [inst : Ring R] [inst_1 : AddCommGroup V]
  [inst_2 : Module R V] [inst_3 : TopologicalSpace P] [inst_4 : AddTorsor V P] [inst_5 : AddCommGroup W]
  [inst_6 : Module R W] [inst_7 : TopologicalSpace Q] [inst_8 : AddTorsor W Q] {W₂ : Type u_6} {Q₂ : Type u_7}
  [inst_9 : AddCommGroup W₂] [inst_10 : Module R W₂] [inst_11 : TopologicalSpace Q₂] [inst_12 : AddTorsor W₂ Q₂]
  [inst_13 : TopologicalSpace V] [inst_14 : IsTopologicalAddTorsor P] [inst_15 : TopologicalSpace W]
  [inst_16 : IsTopologicalAddTorsor Q] [inst_17 : TopologicalSpace W₂] [inst_18 : IsTopologicalAddTorsor Q₂]
  (f : P →ᴬ[R] Q) (g : Q →ᴬ[R] Q₂), (g.comp f).contLinear = g.contLinear ∘SL f.contLinear

Defined in

Mathlib.Topology.Algebra.ContinuousAffineMap

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleTopologicalSpaceAddTorsorAddCommGroupModuleTopologicalSpaceAddTorsorAddCommGroupModuleTopologicalSpaceAddTorsorTopologicalSpaceIsTopologicalAddTorsorTopologicalSpaceIsTopologicalAddTorsorTopologicalSpaceIsTopologicalAddTorsor