Theorems · Theorem · dynamical systems
IsOpen.iUnion_smul
∀ (G : Type u_2) {α : Type u_3} [inst : Group G] [inst_1 : TopologicalSpace α] [inst_2 : MulAction G α]
[MulAction.IsMinimal G α] {U : Set α}, IsOpen U → U.Nonempty → ⋃ g, g • U = Set.univ- Defined in
- Mathlib.Dynamics.Minimal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Set.univstatement · cited by 3,945
- Set.Nonemptystatement and proof · cited by 2,627
- Set.iUnionstatement · cited by 2,483
- IsOpenstatement and proof · cited by 2,400
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- inv_smul_smulproof · cited by 76
- Set.iUnion_eq_univ_iffproof · cited by 19
- MulAction.IsMinimalstatement and proof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- IsCompact.exists_finite_cover_smulproof · cited by 1