{
  "id": "2409.04939",
  "version": "v1",
  "published": "2024-09-08T01:08:34.000Z",
  "updated": "2024-09-08T01:08:34.000Z",
  "title": "The further study on the category of T-convergence groups",
  "authors": [
    "Lingqiang Li",
    "Qiu Jin"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "T-convergence groups is a natural extension of lattice-valued topological groups, which is a newly introduced mathematical structure. In this paper, we will further explore the theory of T-convergence groups. The main results include: (1) It possesses a novel characterization through the $\\odot$-product of T-filters, and it is localizable, meaning that each T-convergence group is uniquely determined by the convergence at the identity element of the underlying group. (2) The definition of its subcategory, the topological T-convergence groups, can be simplified by removing the topological condition (TT). (3) It exhibits uniformization, which means that each T-convergence group can be reconstructed from a T-uniformly convergent space. (4) It possesses a power object, indicating that it has good category properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-08T01:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "identity element",
      "main results",
      "novel characterization",
      "natural extension",
      "topological t-convergence groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}