Theorems · Theorem · Lie groups
AddSubgroup.isOpen_mono
∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousAdd G] {H₁ H₂ : AddSubgroup G},
H₁ ≤ H₂ → IsOpen ↑H₁ → IsOpen ↑H₂- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- IsOpen.mem_nhdsproof · cited by 470
- Filter.mem_of_supersetproof · cited by 308
- ZeroMemClass.zero_memproof · cited by 162
- SeparatelyContinuousAddstatement and proof · cited by 83
- AddSubgroup.isOpen_of_mem_nhdsproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.isOpen_monoproof · cited by 1
- AddSubgroup.isOpen_of_openAddSubgroupproof · cited by 0
- IsLocalRing.isOpen_iff_finite_quotientproof · cited by 0
- ProfiniteGrp.closedAddSubgroup_eq_sInf_openproof · cited by 0