Theorems · Theorem · general topology

SeparationQuotient.mkCLM_comp_outCLM

∀ (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],
  SeparationQuotient.mkCLM K E ∘SL SeparationQuotient.outCLM K E = ContinuousLinearMap.id K (SeparationQuotient E)

Defined in: Mathlib.Topology.Algebra.SeparationQuotient.Section
Cited by: 2 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module TopologicalSpace IsTopologicalAddGroup ContinuousConstSMul

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Cites14

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
ContinuousLinearMapstatement · cited by 5,352
IsTopologicalAddGroupstatement and proof · cited by 1,394
DivisionRingstatement and proof · cited by 1,062
ContinuousConstSMulstatement and proof · cited by 832
ContinuousLinearMap.compstatement · cited by 709
ContinuousLinearMap.idstatement · cited by 233
SeparationQuotientstatement · cited by 128
SeparationQuotient.outCLMstatement · cited by 11

Cited by2

Results whose statement or proof uses this declaration.

SeparationQuotient.mk_outCLMproof · cited by 4
SeparationQuotient.postcomp_mkCLM_surjectiveproof · cited by 1