Continuous lattices of partitions and lattices of continuous partitions (Q2764192)

The paper describes connections between the theory of continuous (measurable) partitions and the asymptotic theory of finite partition lattices. In particular: (i) the Björner continuous partition lattice is realized as a subsemilattice of measurable partitions in the sense of V. A. Rokhlin; (ii) for any homogeneous equivalence relation a continuous lattice is constructed and a rank function on this lattice is defined, (iii) the representation of these lattices in the von Neumann factors of type \(\text{II}_1\) is described. This representation generalizes linear realizations of continuous matroids.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00033].