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arXiv · 1011.1869

Rothberger bounded groups and Ramsey theory

Marion Scheepers
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Abstract

We show that: 1. Rothberger bounded subgroups of sigma-compact groups are characterized by Ramseyan partition relations. 2. For each uncountable cardinal $κ$ there is a ${\sf T}_0$ 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 subspace of any sigma-compact space. 3. For each uncountable cardinal $κ$ there is a ${\sf T}_0$ 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.

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Marion Scheepers. 2010-11-08. Rothberger bounded groups and Ramsey theory. https://arxiv.org/abs/1011.1869

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