Theorems · Theorem · Lie groups
QuotientAddGroup.discreteTopology
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [SeparatelyContinuousAdd G] {N : AddSubgroup G},
IsOpen ↑N → DiscreteTopology (G ⧸ N)- Defined in
- Mathlib.Topology.Algebra.Group.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- IsOpenstatement and proof · cited by 2,400
- HasQuotient.Quotientstatement · cited by 2,301
- DiscreteTopologystatement · cited by 373
- SeparatelyContinuousAddstatement and proof · cited by 83
- QuotientAddGroup.discreteTopology_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- OpenAddSubgroup.isClosedproof · cited by 3
- AddSubgroup.quotient_finite_of_isOpenproof · cited by 2