Theorems · Theorem · dynamical systems
dense_of_nonempty_smul_invariant
∀ (M : Type u_1) {α : Type u_3} [inst : Monoid M] [inst_1 : TopologicalSpace α] [inst_2 : MulAction M α]
[MulAction.IsMinimal M α] {s : Set α}, s.Nonempty → (∀ (c : M), c • s ⊆ s) → Dense s- 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.
Cites11
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
- Monoidstatement and proof · cited by 3,887
- Set.Nonemptystatement and proof · cited by 2,627
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- Densestatement and proof · cited by 359
- Set.range_subset_iffproof · cited by 99
- Dense.monoproof · cited by 43
- MulAction.IsMinimalstatement and proof · cited by 16
- MulAction.dense_orbitproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- eq_empty_or_univ_of_smul_invariant_closedproof · cited by 1