There is a proper Baire category preserving forcing which adds infinitely equal real but no Cohen real. This resolves a long-standing open problem of David Fremlin. The forcing has a natural description in terms of infinite-dimensional topology.

We conclude the discussion of additivity, Baire number, uniformity and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cicho´n's diagram.

We establish fairly general sufficient conditions for a locally compact group (a Baire topological group) to admit partitions into finitely many congruent μ-thick (everywhere of second category) subsets.

Let G be a closed subgroup of S∞ and X be a Polish G-space. To each x ∈ X we associate an admissible set Ax and show how questions about X which involve Baire category, can be formalized in Ax.