Representations of commutative semigroups by products of metric -dimensional spaces
Representations of presheaves of semiuniformisable spaces, and representation of a presheaf by the presheaf of all continuous sections in its covering-space
Residuality of the set of embeddings into Nagata's n-dimensional universal spaces
Residually finite congruences and quasi-regular subsets in uniform algebras
Resolving a question of Arkhangel'skiĭ's
We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.
Results and problems concerning compactifications, compact subtopologies, and mappings
Rétractions dans les espaces stratifiables
Rosenthal compacta and NIP formulas
We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about ϕ-types for ϕ NIP. In particular, we show that if M is a countable model, then an M-invariant ϕ-type is Borel-definable. Also, the space of M-invariant ϕ-types is a Rosenthal compactum, which implies a number of topological tameness properties.