Theorems · Theorem · Lie groups
QuotientGroup.discreteTopology_iff
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [SeparatelyContinuousMul G] {N : Subgroup G},
DiscreteTopology (G ⧸ N) ↔ IsOpen ↑N- Defined in
- Mathlib.Topology.Algebra.Group.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.preimageproof · cited by 4,946
- Subgroupstatement and proof · cited by 3,593
- IsOpenstatement and proof · cited by 2,400
- HasQuotient.Quotientstatement and proof · cited by 2,301
- DiscreteTopologystatement and proof · cited by 373
- QuotientGroup.mkproof · cited by 196
- SeparatelyContinuousMulstatement and proof · cited by 133
- isOpen_coinducedproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- QuotientGroup.discreteTopologyproof · cited by 2
- Subgroup.isOpen_of_isClosed_of_finiteIndexproof · cited by 2