Topology on sets of von-Neumann algebras

In this talk, we will be studying the Effros-Marechal topology on sets of von-Neumann algebras, in particular showing that the topology is Polish. Further, we will have a quick look at the some of the key results proved by Haagerup and Winslow, and contrast them with some of our results, particularly on sets of von Neumann algebras with appropriate approximation properties. We will end by studying the set of MASAs in hyperfinite factor under this topology, showing that the generic MASA is singular.