Theorems · Theorem · Lie groups
ProfiniteGrp.exist_openNormalSubgroup_sub_open_nhds_of_one
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [IsTopologicalGroup G] [CompactSpace G]
[TotallyDisconnectedSpace G] {U : Set G}, IsOpen U → 1 ∈ U → ∃ H, ↑H ⊆ U- Defined in
- Mathlib.Topology.Algebra.ClopenNhdofOne
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- IsOpenstatement and proof · cited by 2,400
- le_reflproof · cited by 2,061
- CompactSpacestatement and proof · cited by 593
- IsTopologicalGroupstatement and proof · cited by 469
- TotallyDisconnectedSpacestatement and proof · cited by 295
- IsClopenproof · cited by 189
- mem_nhds_iffproof · cited by 67
- OpenNormalSubgroupstatement and proof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- ProfiniteGrp.closedSubgroup_eq_sInf_openproof · cited by 0
- ProfiniteGrp.toLimit_injectiveproof · cited by 0
- Ideal.Quotient.stabilizerHom_surjective_of_profiniteproof · cited by 0
- Algebra.IsInvariant.exists_smul_of_under_eq_of_profiniteproof · cited by 0
- Algebra.IsInvariant.isIntegral_of_profiniteproof · cited by 0