Rothberger bounded groups and Ramsey theory

Details Rothberger bounded groups and Ramsey theory Rothberger bounded groups and Ramsey theory

2010-11-08

arxiv.org/abs/1011.1869v1

Mathematics

General Topology

11 pages

Scientific paper

We show that: 1. Rothberger bounded subgroups of sigma-compact groups are characterized by Ramseyan partition relations. 2. For each uncountable cardinal $\kappa$ there is a ${\sf T}_0$ topological group of cardinality $\kappa$ 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 $\kappa$ there is a ${\sf T}_0$ topological group of cardinality $\kappa$ such that ONE has a winning strategy in the point-open game on the group and the group is \sigma-compact.

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