Beschreibung:
Abstract We prove some “universality” results for topological dynamical systems. In particular, we show that for any continuous self-map 𝑇 of a perfect Polish space, one can find a dense, 𝑇-invariant set homeomorphic to the Baire space ℕℕ; that there exists a bounded linear operator 𝑈: ℓ ⟶ ℓ such that any linear operator 𝑇 from a separable Banach space into itself with ‖𝑇‖ ≤ 1 is a linear factor of 𝑈; and that given any 𝜎-compact family ℱ of continuous self-maps of a compact metric space, there is a continuous self-map 𝑈ℱ of ℕℕ such that each 𝑇 ∈ ℱ is a factor of 𝑈ℱ.