Theorems · Theorem · Lie groups
IsOpen.neg
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : InvolutiveNeg G] [ContinuousNeg G] {s : Set G},
IsOpen s → IsOpen (-s)- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- IsOpenstatement and proof · cited by 2,400
- Set.negstatement · cited by 168
- InvolutiveNegstatement and proof · cited by 151
- IsOpen.preimageproof · cited by 147
- ContinuousNegstatement and proof · cited by 119
- ContinuousNeg.continuous_negproof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- IsOpen.add_closureproof · cited by 3
- IsOpen.closure_addproof · cited by 1
- IsTopologicalAddGroup.exists_addNegClosureNhdproof · cited by 1
- IsOpen.smul_sphereproof · cited by 0
- IsOpen.closure_subproof · cited by 0