Theorems · Definition · Lie groups
OpenNormalSubgroup.toOpenSubgroup
{G : Type u} → [inst : Group G] → [inst_1 : TopologicalSpace G] → OpenNormalSubgroup G → OpenSubgroup G- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- GroupTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Groupstatement and proof · cited by 6,238
- OpenSubgroupstatement · cited by 47
- OpenNormalSubgroupstatement and proof · cited by 27
Cited by15
Results whose statement or proof uses this declaration.
- ProfiniteGrp.toFiniteQuotientFunctorproof · cited by 3
- OpenNormalSubgroup.extstatement and proof · cited by 2
- OpenNormalSubgroup.toFiniteIndexNormalSubgroupproof · cited by 2
- ProfiniteGrp.denseRange_toLimitproof · cited by 1
- Ideal.Quotient.stabilizerHomSurjectiveAuxFunctorproof · cited by 1
- OpenNormalSubgroup.isNormal'statement · cited by 1
- OpenNormalSubgroup.toSubgroup_injectivestatement and proof · cited by 1
- ProfiniteGrp.ProfiniteCompletion.quotientMapstatement and proof · cited by 1
- ProfiniteGrp.closedSubgroup_eq_sInf_openproof · cited by 0
- ProfiniteGrp.toLimitFun_continuousproof · cited by 0
- Algebra.IsInvariant.exists_smul_of_under_eq_of_profiniteproof · cited by 0
- Algebra.IsInvariant.isIntegral_of_profiniteproof · cited by 0