2024/06/26 by Jian Li, Xianjuan Liang, Li, Jian +3
Computer Science · Mathematics · #Advanced Database Systems and Queries #Computer science #Geometry #Mathematics #Product (mathematics)
paper · pdf · doi:10.4064/fm241006-2-1
openalex created_date 2024/06/28 · openalex publication_date 2026/05/29 · openalex updated_date 2026/07/28
Let G be a countable infinite discrete group. We show that a subset F of G contains a return time set of some piecewise syndetic recurrent point x in a compact Hausdorff space X with a G-action if and only if F is a quasi-central set. As an application, we show that if a nonempty closed subsemigroup S of the Stone–Čech compactification βG contains the smallest ideal K(βG) of βG then S-product recurrence is equivalent to distality, which partially answers a question of Auslander and Furstenberg [Trans. Amer. Math. Soc. 343 (1994), 221–232].