Theorems · Theorem · Lie groups
IsTopologicalGroup.exist_openNormalSubgroup_sub_clopen_nhds_of_one
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [IsTopologicalGroup G] [CompactSpace G] {W : Set G},
IsClopen W → 1 ∈ W → ∃ H, ↑H ⊆ W- Defined in
- Mathlib.Topology.Algebra.ClopenNhdofOne
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Subgroupproof · cited by 3,593
- CompactSpacestatement and proof · cited by 593
- IsTopologicalGroupstatement and proof · cited by 469
- IsClopenstatement and proof · cited by 189
- Subgroup.FiniteIndexproof · cited by 113
- OpenSubgroupproof · cited by 47
- OpenSubgroup.toSubgroupproof · cited by 34
- OpenNormalSubgroupstatement · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- ProfiniteGrp.exist_openNormalSubgroup_sub_open_nhds_of_oneproof · cited by 5