Quasi-disjointness in topological dynamics

Hui Xu; Xiangdong Ye

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arXiv · 2605.30066

Quasi-disjointness in topological dynamics

Hui Xu·Xiangdong Ye

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Abstract

Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is preserved under taking factors, proximal extensions, and group extensions. As a consequence, we establish that every minimal {\bf PI} system is quasi-disjoint from all minimal systems. In addition, some variant of quasi-disjointness, namely strong quasi-disjointness is also introduced and examined. Particularly, we prove that each {\bf AI} system is strongly quasi-disjoint from all minimal systems.

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Hui Xu, Xiangdong Ye. 2026-05-28. Quasi-disjointness in topological dynamics. https://arxiv.org/abs/2605.30066

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