Year: 2026
Type: article
Abstract: 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].
Source: Fundamenta Mathematicae
DOI: 10.4064/fm241006-2-1
Authors: Jian Li, Xianjuan Liang, Yini Yang
Institutions: Shantou University, Yunnan Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G239404273, G8067489827
OpenAlex ID: W4400104715