Theorems · Theorem · Lie groups
IsClosed.mul_closure_one_eq
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [IsTopologicalGroup G] {F : Set G},
IsClosed F → F * closure {1} = F- Defined in
- Mathlib.Topology.Algebra.Group.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- mul_oneproof · cited by 3,885
- IsClosedstatement and proof · cited by 1,639
- closurestatement and proof · cited by 1,254
- Set.image_congrproof · cited by 533
- IsTopologicalGroupstatement and proof · cited by 469
- Set.mulstatement · cited by 297
- Set.Subset.antisymmproof · cited by 213
- IsClosed.closure_eqproof · cited by 139
- Set.image_id'proof · cited by 86
Cited by1
Results whose statement or proof uses this declaration.
- IsOpen.mul_closure_one_eqproof · cited by 1