{
  "id": "2308.09557",
  "version": "v1",
  "published": "2023-08-18T13:40:51.000Z",
  "updated": "2023-08-18T13:40:51.000Z",
  "title": "Spaces not distinguishing ideal pointwise and $σ$-uniform convergence",
  "authors": [
    "Rafał Filipów",
    "Adam Kwela"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We examine topological spaces not distinguishing ideal pointwise and ideal $\\sigma$-uniform convergence of sequences of real-valued continuous functions defined on them. For instance, we introduce a purely combinatorial cardinal characteristic (a sort of the bounding number $\\mathfrak{b}$) and prove that it describes the minimal cardinality of topological spaces which distinguish ideal pointwise and ideal $\\sigma$-uniform convergence. Moreover, we provide examples of topological spaces (focusing on subsets of reals) that do or do not distinguish the considered convergences. Since similar investigations for ideal quasi-normal convergence instead of ideal $\\sigma$-uniform convergence have been performed in literature, we also study spaces not distinguishing ideal quasi-normal and ideal $\\sigma$-uniform convergence of sequences of real-valued continuous functions defined on them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-18T13:40:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C30",
      "40A35",
      "03E17",
      "40A30",
      "26A03",
      "54A20",
      "03E35"
    ],
    "keywords": [
      "uniform convergence",
      "distinguishing ideal pointwise",
      "topological spaces",
      "real-valued continuous functions",
      "ideal quasi-normal convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}