Rothberger bounded groups and Ramsey theory
Copyright policy )Rothberger bounded groups and Ramsey theory
We show that: 1. Rothberger bounded subgroups of sigma-compact groups are characterized by Ramseyan partition relations. 2. For each uncountable cardinal $��$ there is a ${\sf T}_0$ topological group of cardinality $��$ 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 $��$ there is a ${\sf T}_0$ topological group of cardinality $��$ such that ONE has a winning strategy in the point-open game on the group and the group is ��-compact.
11 pages
- Boise State University United States
Noncompact covering properties (paracompact, Lindelöf, etc.), Group Theory (math.GR), Topological group, 510, FOS: Mathematics, Partition relations, Mathematics - General Topology, topological group, Infinite game, Rothberger bounded, Ramsey theory, infinite game, General Topology (math.GN), Uniformizable space, strong measure zero, Other combinatorial set theory, BRC, 004, Structure of general topological groups, 03E02, 03E05, 05D10, 22A05, 54D20, 54G10, 54H11, Geometry and Topology, uniformizable space, Mathematics - Group Theory, Mathematics, Strong measure zero, Topological groups (topological aspects)
Noncompact covering properties (paracompact, Lindelöf, etc.), Group Theory (math.GR), Topological group, 510, FOS: Mathematics, Partition relations, Mathematics - General Topology, topological group, Infinite game, Rothberger bounded, Ramsey theory, infinite game, General Topology (math.GN), Uniformizable space, strong measure zero, Other combinatorial set theory, BRC, 004, Structure of general topological groups, 03E02, 03E05, 05D10, 22A05, 54D20, 54G10, 54H11, Geometry and Topology, uniformizable space, Mathematics - Group Theory, Mathematics, Strong measure zero, Topological groups (topological aspects)
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