{
  "id": "2506.17716",
  "version": "v1",
  "published": "2025-06-21T13:34:39.000Z",
  "updated": "2025-06-21T13:34:39.000Z",
  "title": "Topological groups from matrices of sets",
  "authors": [
    "Boriša Kuzeljević",
    "Stepan Milošević",
    "Stevo Todorčević"
  ],
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "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 $\\omega_1$-tree is Frech\\'{e}t iff the tree is Aronszajn. We also determine cofinal types of some of these groups under certain set theoretic assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-21T13:34:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological groups",
      "determine cofinal types",
      "set theoretic assumptions",
      "group built",
      "connect topological properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}