Theorems · Theorem · Lie groups
IsTopologicalAddGroup.exist_openAddSubgroup_sub_clopen_nhds_of_zero
∀ {G : Type u_2} [inst : AddGroup G] [inst_1 : TopologicalSpace G] [IsTopologicalAddGroup G] [CompactSpace G]
{W : Set G}, IsClopen W → 0 ∈ W → ∃ H, ↑H ⊆ W- Defined in
- Mathlib.Topology.Algebra.OpenSubgroup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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 · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupproof · cited by 3,232
- LE.le.transproof · cited by 3,151
- Set.iUnionproof · cited by 2,483
- IsOpenproof · cited by 2,400
- zero_addproof · cited by 2,366
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- neg_negproof · cited by 960
- add_assocproof · cited by 746
Cited by1
Results whose statement or proof uses this declaration.