Topological characteristic factors and independence along arithmetic progressions

Abstract

In 1994 Glasner studied the topological characteristic factor for minimal systems. It is shown that up to canonically defined proximal extensions, a characteristic family for τd= T × T2 × ⋯ × Td is the family of canonical PI flows of order d − 1. In this paper, we generalize Glasner’s work to the product system of finitely many minimal systems and give its relative version. As applications, we derive several applications related to independence pairs along arithmetic progressions and Δ-transitivity.