Topological games and products, II
Topological type of weakly closed subgroups in Banach spaces
The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in which are interesting from the Banach space theory point of view are discussed.
Transfinite cardinal dimension and separability
Trivial bundles of spaces of probability measures and countable-dimensionality
The probability measure functor P carries open continuous mappings of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers are infinite. This answers a question raised by V. Fedorchuk.
Two-dimension-like functions defined on the class of all Tychonoff spaces.