The Effros-Marechal topology in the space of von Neumann algebras, II

We continus our study [9] of the Effros-Marechal topology on the space vN(H ) of all von Neumann algebras acting on a fixed separable Hilbert space H. In particular, we prove that factors of each of the types: II1, IIinfinity, and (for fixed lambda is an element of [ 0, 1 ]) IIIlambda, form a dense s ubset of vN(H). Moreover, the density of type I-factors (or, equivalently, of injective factors) in vN(H), is proved to be equivalent to famous conjec tures by A. Connes and E. Kirchberg. (C) 2000 Academic Press.