Theorems · Theorem · Lie groups
Subgroup.isOpen_of_mem_nhds
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [SeparatelyContinuousMul G] (H : Subgroup G) {g : G},
↑H ∈ nhds g → IsOpen ↑H- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 3 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.
Cites21
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
- Groupstatement and proof · cited by 6,238
- Set.ofPredproof · cited by 6,101
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Subgroupstatement and proof · cited by 3,593
- IsOpenstatement · cited by 2,400
- SetLike.mem_coeproof · cited by 302
- continuous_idproof · cited by 192
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.fixingSubgroup_isOpenproof · cited by 5
- Subgroup.isOpen_monoproof · cited by 2
- Subgroup.isOpen_of_one_mem_interiorproof · cited by 0