Theorems · Theorem · general topology

SeparationQuotient.exists_out_continuousLinearMap

∀ (K : Type u_1) (E : Type u_2) [inst : DivisionRing K] [inst_1 : AddCommGroup E] [inst_2 : Module K E]
  [inst_3 : TopologicalSpace E] [inst_4 : IsTopologicalAddGroup E] [inst_5 : ContinuousConstSMul K E],
  ∃ f, SeparationQuotient.mkCLM K E ∘SL f = ContinuousLinearMap.id K (SeparationQuotient E)

There exists a continuous K-linear map from SeparationQuotient E to E such that mk (outCLM x) = x for all x. Note that continuity of this map comes for free, because mk is a topology inducing map.

Defined in

Mathlib.Topology.Algebra.SeparationQuotient.Section

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleTopologicalSpaceIsTopologicalAddGroupContinuousConstSMul