Theorems · Theorem · Lie groups
IsOpen.mul_closure
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [IsTopologicalGroup G] {s : Set G},
IsOpen s → ∀ (t : Set G), s * closure t = s * t- Defined in
- Mathlib.Topology.Algebra.Group.Pointwise
- Cited by
- 2 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.
Cites16
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
- IsOpenstatement and proof · cited by 2,400
- closurestatement and proof · cited by 1,254
- LE.le.antisymmproof · cited by 507
- IsTopologicalGroupstatement and proof · cited by 469
- subset_closureproof · cited by 309
- Set.mulstatement · cited by 297
- inv_mul_cancel_leftproof · cited by 88
- mem_closure_iffproof · cited by 15
- Set.inv_mem_invproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- IsOpen.closure_mulproof · cited by 1
- IsOpen.div_closureproof · cited by 0