6 research outputs found
The combinatorics of the Baer-Specker group
Denote the integers by Z and the positive integers by N.
The groups Z^k (k a natural number) are discrete, and the classification up
to isomorphism of their (topological) subgroups is trivial. But already for the
countably infinite power Z^N of Z, the situation is different. Here the product
topology is nontrivial, and the subgroups of Z^N make a rich source of examples
of non-isomorphic topological groups. Z^N is the Baer-Specker group.
We study subgroups of the Baer-Specker group which possess group theoretic
properties analogous to properties introduced by Menger (1924), Hurewicz
(1925), Rothberger (1938), and Scheepers (1996). The studied properties were
introduced independently by Ko\v{c}inac and Okunev. We obtain purely
combinatorial characterizations of these properties, and combine them with
other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and
Scheepers.Comment: To appear in IJ
Some new directions in infinite-combinatorial topology
We give a light introduction to selection principles in topology, a young
subfield of infinite-combinatorial topology. Emphasis is put on the modern
approach to the problems it deals with. Recent results are described, and open
problems are stated. Some results which do not appear elsewhere are also
included, with proofs.Comment: Small update