Theorems · Theorem · dynamical systems
MulAction.dense_orbit
∀ (M : Type u_1) {α : Type u_3} [inst : Monoid M] [inst_1 : TopologicalSpace α] [inst_2 : MulAction M α]
[MulAction.IsMinimal M α] (x : α), Dense (MulAction.orbit M x)- Defined in
- Mathlib.Dynamics.Minimal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Monoidstatement and proof · cited by 3,887
- MulActionstatement and proof · cited by 1,294
- Densestatement · cited by 359
- MulAction.orbitstatement · cited by 114
- MulAction.IsMinimalstatement and proof · cited by 16
- MulAction.IsMinimal.dense_orbitproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- dense_of_nonempty_smul_invariantproof · cited by 1
- denseRange_smulproof · cited by 1
- ErgodicSMul.trans_isMinimalproof · cited by 0