{
  "id": "2011.03777",
  "version": "v1",
  "published": "2020-11-07T13:49:44.000Z",
  "updated": "2020-11-07T13:49:44.000Z",
  "title": "Ideals generated by families of sequences of natural numbers",
  "authors": [
    "Pratulananda Das",
    "Szymon Głcab",
    "Rafał Filipów",
    "Jacek Tryba"
  ],
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "We consider ideals on $\\omega\\times\\omega$ generated by subsets of $\\omega^\\omega$. Namely, for $\\mathcal{F}\\subset \\omega^\\omega$ we define $$\\mathcal{I}(\\mathcal{F})=\\{A\\subset \\omega\\times\\omega:\\exists f\\in \\mathcal{F}\\,\\forall^\\infty n\\in\\omega\\, (|\\{k:(n,k)\\in A\\}|\\leq f(n))\\}.$$ These ideals encompass other well known ideals e.g.~$fin\\times fin$ and $ED$. We examine some properties of these ideals including topological complexity and cardinal characteristics associated with them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-07T13:49:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "natural numbers",
      "cardinal characteristics",
      "ideals encompass",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}