abstract: Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems, Colloquium Mathematicum 110(1), (2008), 117-150. As a result, some new families emerged. Here, their counterparts in topological dynamics has been considered. The differences will be discussed and new classes of systems in topological dynamics will be introduced.
This presentation is made on behalf of Maliheh Dabbaghian Amiri who cannot attend