Topological characteristic factors along cubes of minimal systems

Abstract

In this paper we study the topological characteristic factors along cubes of minimal systems. It is shown that up to proximal extensions the pro-nilfactors are the topological characteristic factors along cubes of minimal systems. In particular, for a distal minimal system, the maximal $(d-1)$-step pro-nilfactor is the topological cubic characteristic factor of order $d$.

arXiv admin note: text overlap with arXiv:1105.3584; text overlap with arXiv:0905.3098, arXiv:1605.01119 by other authors