@article{Sherman_2007, title={On the dimension theory of von Neumann algebras}, volume={101}, url={https://www.mscand.dk/article/view/15035}, DOI={10.7146/math.scand.a-15035}, abstractNote={In this paper we study three aspects of $(\mathcal{P}(\mathcal{M})/{\sim})$, the set of Murray-von Neumann equivalence classes of projections in a von Neumann algebra $\mathcal M$. First we determine the topological structure that $(\mathcal{P}(\mathcal{M})/{\sim})$ inherits from the operator topologies on $\mathcal M$. Then we show that there is a version of the center-valued trace which extends the dimension function, even when $\mathcal M$ is not $\sigma$-finite. Finally we prove that $(\mathcal{P}(\mathcal{M})/{\sim})$ is a complete lattice, a fact which has an interesting reformulation in terms of representations.}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Sherman, David}, year={2007}, month={Sep.}, pages={123–147} }