Theorems · Theorem · Lie groups
AddSubgroup.quotient_finite_of_isOpen
∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousAdd G] [CompactSpace G]
(U : AddSubgroup G), IsOpen ↑U → Finite (G ⧸ U)- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 2 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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- 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
- SeparatelyContinuousAddstatement and proof · cited by 83
- finite_of_compact_of_discreteproof · cited by 6
- QuotientAddGroup.discreteTopologyproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.quotient_finite_of_isOpen'proof · cited by 0
- IsLocalRing.isOpen_iff_finite_quotientproof · cited by 0