Rothberger Bounded Groups and Ramsey Theory

Authors

Marion Scheepers, Boise State UniversityFollow

Document Type

Article

Publication Date

8-15-2011

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).

Publication Information

Scheepers, Marion. (2011). "Rothberger Bounded Groups and Ramsey Theory". Topology and its Applications, 158(13), 1575-1583. https://doi.org/10.1016/j.topol.2011.05.025