We continue our study [9] of the Effros-Maréchal 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, II_∞, and (for fixed λ∈[0, 1]) III_λ, form a dense subset 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 conjectures by A. Connes and E. Kirchberg.