Theorems · Theorem · general topology
NonarchimedeanGroup.exists_openSubgroup_separating
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [NonarchimedeanGroup G] [T2Space G] {a b : G},
a ≠ b → ∃ V, Disjoint (a • ↑V) (b • ↑V)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
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
- Groupstatement and proof · cited by 6,238
- IsOpenproof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- mul_assocproof · cited by 1,667
- T2Spacestatement and proof · cited by 1,351
- Set.smulSetstatement · cited by 608
- inv_invproof · cited by 494
- IsOpen.mem_nhdsproof · cited by 470
- mul_inv_revproof · cited by 270
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