Theorems · Theorem · functional analysis

ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [CompleteSpace 𝕜]
  [inst_2 : AddCommGroup E] [inst_3 : TopologicalSpace E] [IsTopologicalAddGroup E] [inst_5 : Module 𝕜 E]
  [ContinuousSMul 𝕜 E] [inst_7 : AddCommGroup F] [inst_8 : TopologicalSpace F] [inst_9 : Module 𝕜 F] [T2Space F]
  (f : E →L[𝕜] F) [FiniteDimensional 𝕜 ↥(↑f).range], (↑f).ker.ClosedComplemented

Defined in

Mathlib.Topology.Algebra.Module.FiniteDimension

Cited by

0 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldCompleteSpaceAddCommGroupTopologicalSpaceIsTopologicalAddGroupModuleContinuousSMulAddCommGroupTopologicalSpaceModuleT2SpaceFiniteDimensional