Theorems · Inductive type · dynamical systems
MulAction.IsMinimal
(M : Type u_1) → (α : Type u_2) → [inst : Monoid M] → [TopologicalSpace α] → [MulAction M α] → Prop
An action of a monoid M on a topological space is called minimal if the M-orbit of every
point x : α is dense.
- Defined in
- Mathlib.Dynamics.Minimal
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- Monoidstatement · cited by 3,887
- MulActionstatement · cited by 1,294
Cited by18
Results whose statement or proof uses this declaration.
- MulAction.dense_orbitstatement and proof · cited by 3
- IsOpen.exists_smul_memstatement and proof · cited by 3
- eq_empty_or_univ_of_smul_invariant_closedstatement and proof · cited by 1
- denseRange_smulstatement and proof · cited by 1
- IsOpen.iUnion_smulstatement and proof · cited by 1
- IsCompact.exists_finite_cover_smulstatement and proof · cited by 1
- dense_of_nonempty_smul_invariantstatement and proof · cited by 1
- MulAction.IsMinimal.dense_orbitstatement and proof · cited by 1
- MeasureTheory.measure_pos_iff_nonempty_of_smulInvariantstatement and proof · cited by 1
- MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_compact_ne_zerostatement and proof · cited by 1
- MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zerostatement and proof · cited by 1
- IsOpen.iUnion_preimage_smulstatement and proof · cited by 0