Approximation in ergodic theory, Borel, and Cantor dynamics
  This survey is focused on the results related to topologies on the groups of transformations in ergodic theory, Borel, and Cantor dynamics. Various topological properties (density, connectedness, genericity) of these groups and their subsets (subgroups) are studied. 
S. Bezuglyi, J. Kwiatkowski, and K. Medynets