Theorems · Theorem · functional analysis

ContinuousLinearMap.coprod_inl_inr

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} [inst : Semiring R] [inst_1 : TopologicalSpace M]
  [inst_2 : TopologicalSpace N] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : ContinuousAdd M]
  [inst_6 : AddCommMonoid N] [inst_7 : Module R N] [inst_8 : ContinuousAdd N],
  (ContinuousLinearMap.inl R M N).coprod (ContinuousLinearMap.inr R M N) = ContinuousLinearMap.id R (M × N)

Defined in

Mathlib.Topology.Algebra.Module.ContinuousLinearMap.PiProd

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringTopologicalSpaceTopologicalSpaceAddCommMonoidModuleContinuousAddAddCommMonoidModuleContinuousAdd