Theorems · Theorem · Lie groups
closure_submonoidClosure_eq_closure_subgroupClosure
∀ {G : Type u_1} [inst : Group G] [inst_1 : TopologicalSpace G] [CompactSpace G] [IsTopologicalGroup G] (s : Set G),
closure ↑(Submonoid.closure s) = closure ↑(Subgroup.closure s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Subgroupstatement · cited by 3,593
- Submonoidstatement · cited by 3,086
- closurestatement · cited by 1,254
- CompactSpacestatement and proof · cited by 593
- IsTopologicalGroupstatement and proof · cited by 469
- Subgroup.closurestatement · cited by 196
- Submonoid.closurestatement · cited by 167
- topologicalClosure_subgroupClosure_toSubmonoidproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- dense_submonoidClosure_iff_subgroupClosureproof · cited by 0