Theorems · Theorem · dynamical systems
MulAction.isTopologicallyTransitive_iff
∀ (M : Type u_1) {α : Type u_2} [inst : TopologicalSpace α] [inst_1 : Monoid M] [inst_2 : MulAction M α],
MulAction.IsTopologicallyTransitive M α ↔
∀ {U V : Set α}, IsOpen U → U.Nonempty → IsOpen V → V.Nonempty → ∃ m, (m • U ∩ V).Nonempty- Defined in
- Mathlib.Dynamics.Transitive
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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Cites9
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
- IsOpenstatement and proof · cited by 2,400
- MulActionstatement and proof · cited by 1,294
- Set.smulSetstatement · cited by 608
- MulAction.IsTopologicallyTransitivestatement and proof · cited by 8
- MulAction.IsTopologicallyTransitive.exists_smul_interproof · cited by 2
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