Theorems · Theorem · Lie groups
IsOpen.add_closure
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] {s : Set G},
IsOpen s → ∀ (t : Set G), s + closure t = s + t- Defined in
- Mathlib.Topology.Algebra.Group.Pointwise
- Cited by
- 3 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
- AddGroupstatement and proof · cited by 4,410
- IsOpenstatement and proof · cited by 2,400
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- closurestatement and proof · cited by 1,254
- LE.le.antisymmproof · cited by 507
- Set.addstatement · cited by 338
- subset_closureproof · cited by 309
- neg_add_cancel_leftproof · cited by 84
- mem_closure_iffproof · cited by 15
- Set.neg_mem_negproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Convex.combo_interior_closure_subset_interiorproof · cited by 3
- IsOpen.closure_addproof · cited by 1
- IsOpen.sub_closureproof · cited by 0