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<p>We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these objects. For example, the group built from an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\omega _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ω</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-tree is Fréchet if and only if the tree is Aronszajn. We also determine cofinal types of some of these groups under certain set theoretic assumptions.</p>

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Topological groups from matrices of sets

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Boriša Kuzeljević,
  • Stepan Milošević,
  • Stevo Todorčević

摘要

We give a general construction of topological groups from combinatorial structures such as trees, towers, gaps, and subadditive functions. We connect topological properties of corresponding groups with combinatorial properties of these objects. For example, the group built from an \(\omega _1\) ω 1 -tree is Fréchet if and only if the tree is Aronszajn. We also determine cofinal types of some of these groups under certain set theoretic assumptions.