Theorems · Theorem · Lie groups
IsOpen.inv
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : InvolutiveInv G] [ContinuousInv G] {s : Set G},
IsOpen s → IsOpen s⁻¹- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 4 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
- IsOpen.preimageproof · cited by 147
- Set.invstatement · cited by 132
- InvolutiveInvstatement and proof · cited by 102
- ContinuousInvstatement and proof · cited by 89
- ContinuousInv.continuous_invproof · cited by 27
Cited by4
Results whose statement or proof uses this declaration.
- IsOpen.mul_closureproof · cited by 2
- IsOpen.closure_mulproof · cited by 1
- IsTopologicalGroup.exists_mulInvClosureNhdproof · cited by 1
- IsOpen.closure_divproof · cited by 0