Resumen de On the dimension theory of von Neumann algebras
In this paper we study three aspects of (P(M)/∼), the set of Murray-von Neumann equivalence classes of projections in a von Neumann algebra M. First we determine the topological structure that (P(M)/∼) inherits from the operator topologies on M. Then we show that there is a version of the center-valued trace which extends the dimension function, even when M is not σ-finite. Finally we prove that (P(M)/∼) is a complete lattice, a fact which has an interesting reformulation in terms of representations.
