Theorems · Theorem · functional analysis

ContinuousLinearMap.toLinearMap_ofIsTopCompl

∀ {R : Type u_1} [inst : Ring R] {E : Type u_2} {F : Type u_3} [inst_1 : TopologicalSpace E] [inst_2 : AddCommGroup E]
  [inst_3 : Module R E] [inst_4 : IsTopologicalAddGroup E] [inst_5 : TopologicalSpace F] [inst_6 : AddCommGroup F]
  [inst_7 : Module R F] [inst_8 : ContinuousAdd F] {p q : Submodule R E} (h : Submodule.IsTopCompl p q) (φ : ↥p →L[R] F)
  (ψ : ↥q →L[R] F), ↑(ContinuousLinearMap.ofIsTopCompl h φ ψ) = LinearMap.ofIsCompl ⋯ ↑φ ↑ψ

Defined in

Mathlib.Topology.Algebra.Module.Complement

Cited by

0 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceAddCommGroupModuleIsTopologicalAddGroupTopologicalSpaceAddCommGroupModuleContinuousAdd