Theorems · Theorem · Lie groups
IsClosed.neg
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : InvolutiveNeg G] [ContinuousNeg G] {s : Set G},
IsClosed s → IsClosed (-s)- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
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
- IsClosedstatement and proof · cited by 1,639
- Set.negstatement · cited by 168
- InvolutiveNegstatement and proof · cited by 151
- IsClosed.preimageproof · cited by 138
- ContinuousNegstatement and proof · cited by 119
- ContinuousNeg.continuous_negproof · cited by 37
Cited by2
Results whose statement or proof uses this declaration.
- exists_closed_nhds_zero_neg_eq_add_subsetproof · cited by 3