The combinatorics of the Baer-Specker group

Details The combinatorics of the Baer-Specker group The combinatorics of the Baer-Specker group

2005-08-08

arxiv.org/abs/math/0508146v6

Israel Journal of Mathematics 168 (2008), 125-151

Mathematics

General Topology

To appear in IJM

Scientific paper

10.1007/s11856-008-1060-8

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.

Affiliated with

Also associated with

No associations

Rating

The combinatorics of the Baer-Specker group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The combinatorics of the Baer-Specker group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The combinatorics of the Baer-Specker group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-362255