Theorems · Theorem · Lie groups
IsDiscrete.exists_nhds_eq_zero_of_image_addRight_inter_nonempty
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] (S : AddSubgroup G),
IsDiscrete ↑S → ∃ U ∈ nhds 0, -U = U ∧ ∀ g ∈ S, ((fun x => x + g) '' U ∩ U).Nonempty → g = 0- Defined in
- Mathlib.Topology.Algebra.Group.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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.imagestatement and proof · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Set.Nonemptystatement and proof · cited by 2,627
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- neg_eq_zeroproof · cited by 171
- Set.negstatement · cited by 168
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsQuotientMap.isAddQuotientCoveringMap_of_addSubgroupOpproof · cited by 1