Theorems · Theorem · Lie groups
Subgroup.isOpen_of_isClosed_of_finiteIndex
∀ {G : Type u} [inst : Group G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousMul G] (H : Subgroup G)
[H.FiniteIndex], IsClosed ↑H → IsOpen ↑H- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- IsOpenstatement · cited by 2,400
- IsClosedstatement and proof · cited by 1,639
- SeparatelyContinuousMulstatement and proof · cited by 133
- Subgroup.FiniteIndexstatement and proof · cited by 113
- QuotientGroup.discreteTopology_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsTopologicalGroup.exist_openNormalSubgroup_sub_clopen_nhds_of_oneproof · cited by 1
- Subgroup.discreteTopology_iff_of_finiteIndexproof · cited by 1