Rothberger Bounded Groups and Ramsey Theory
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
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