Theorems · Theorem · Lie groups
AddSubgroup.isOpen_of_mem_nhds
∀ {G : Type u_1} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousAdd G] (H : AddSubgroup G)
{g : G}, ↑H ∈ nhds g → IsOpen ↑H- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- AddGroupstatement and proof · cited by 4,410
- Filter.Tendstoproof · cited by 3,814
- AddSubgroupstatement and proof · cited by 3,232
- IsOpenstatement · cited by 2,400
- SetLike.mem_coeproof · cited by 302
- continuous_idproof · cited by 192
Cited by5
Results whose statement or proof uses this declaration.
- AddSubgroup.isOpen_monoproof · cited by 4
- IsLinearTopology.hasBasis_open_submoduleproof · cited by 2
- IsLinearTopology.hasBasis_open_twoSidedIdealproof · cited by 1
- IsLinearTopology.hasBasis_open_subbimoduleproof · cited by 0
- AddSubgroup.isOpen_of_zero_mem_interiorproof · cited by 0