Theorems · Theorem · dynamical systems

AddAction.isTopologicallyTransitive_iff

∀ (M : Type u_1) {α : Type u_2} [inst : TopologicalSpace α] [inst_1 : AddMonoid M] [inst_2 : AddAction M α],
  AddAction.IsTopologicallyTransitive M α ↔
    ∀ {U V : Set α}, IsOpen U → U.Nonempty → IsOpen V → V.Nonempty → ∃ m, ((m +ᵥ U) ∩ V).Nonempty

Defined in

Mathlib.Dynamics.Transitive

Cited by

1 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

TopologicalSpaceAddMonoidAddAction