Theorems · Theorem · Lie groups
IsTopologicalGroup.exists_mulInvClosureNhd
∀ {G : Type u_1} [inst : TopologicalSpace G] [inst_1 : Group G] [IsTopologicalGroup G] [CompactSpace G] {W : Set G},
IsClopen W → ∃ T, IsTopologicalGroup.mulInvClosureNhd T W- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Groupstatement and proof · cited by 6,238
- nhdsproof · cited by 5,554
- IsOpenproof · cited by 2,400
- CompactSpacestatement and proof · cited by 593
- inv_invproof · cited by 494
- IsOpen.mem_nhdsproof · cited by 470
- IsTopologicalGroupstatement and proof · cited by 469
- Set.inter_subset_leftproof · cited by 360
- Set.inter_commproof · cited by 291
- IsClopenstatement and proof · cited by 189
Cited by1
Results whose statement or proof uses this declaration.
- IsTopologicalGroup.exist_openSubgroup_sub_clopen_nhds_of_oneproof · cited by 1