THE EFFROS-MARECHAL TOPOLOGY IN THE SPACE OF VON-NEUMANN-ALGEBRAS

New concepts of limes inferior and limes superior in the space of von Neumann algebras on a fixed Hilbert space are defined, and the topolog y corresponding to these notions is related to earlier works of Effros and Marechal. A main technical result is that the commutant operation is a homeomorphism on the space of von Neumann algebras with this top ology. Further, the topological properties of several classes and type s of von Neumann factors (regarded as subspaces) are determined, and a lso continuity-type results for Tomita-Takesaki theory are proved. Som e applications to subfactor theory are given.