Article
Rothberger Bounded Groups and Ramsey Theory
Topology and its Applications
Document Type
Article
Publication Date
8-15-2011
Disciplines
Abstract
We show that:
(1) Rothberger bounded subgroups of σ-compact groups are characterized by Ramseyan partition relations (Corollary 4).
(2) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is not a closed subspace of any σ-compact space (Theorem 8).
(3) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ONE has a winning strategy in the point-open game on the group and the group is σ-compact (Corollary 17).
Citation Information
Marion Scheepers. "Rothberger Bounded Groups and Ramsey Theory" Topology and its Applications (2011) Available at: http://works.bepress.com/marion_scheepers/3/