Theorems · Theorem · Lie groups
Subgroup.quotient_finite_of_isOpen
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousMul G] [CompactSpace G]
(U : Subgroup G), IsOpen ↑U → Finite (G ⧸ U)- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finitestatement · cited by 3,029
- IsOpenstatement and proof · cited by 2,400
- HasQuotient.Quotientstatement and proof · cited by 2,301
- CompactSpacestatement and proof · cited by 593
- DiscreteTopologyproof · cited by 373
- SeparatelyContinuousMulstatement and proof · cited by 133
- finite_of_compact_of_discreteproof · cited by 6
- QuotientGroup.discreteTopologyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.quotient_finite_of_isOpen'proof · cited by 1