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Topological minimal self-joinings

Abstract There is an interesting duality between some of the concepts of ergodic theory and those of topological dynamics. This paper is a first attempt at developing a topological analogue to the measure-theoretic notion of a transformation having minimal self-joinings. The main problem is to understand the dynamics of the composition of a cartesian product of powers of a transformation having topological minimal self-joinings with a compact permutation of the coordinates. Most of the results are about the minimal subsets of such a composition.