{
  "id": "2308.12799",
  "version": "v1",
  "published": "2023-08-24T13:58:20.000Z",
  "updated": "2023-08-24T13:58:20.000Z",
  "title": "On $π$-compatible topologies and their special cases",
  "authors": [
    "Vitalij A. Chatyrko"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Topologies $\\tau, \\sigma$ on a set $X$ are called $\\pi$-compatible if $\\tau$ is a $\\pi$-network for $\\sigma$, and vice versa. If topologies $\\tau, \\sigma$ on a set $X$ are $\\pi$-compatible then the families of nowhere dense sets (resp. meager sets or sets possessing the Baire property) of the spaces $(X, \\tau)$ and $(X, \\sigma)$ coincide. A topology $\\sigma$ on a set $X$ is called an admissible extension of a topology $\\tau$ on $X$ if $\\tau \\subseteq \\sigma$ and $\\tau$ is a $\\pi$-network for $\\sigma$. It turns out that examples of admissible extensions were occurred in literature several times. In the paper we provide some new facts about the $\\pi$-compatibility and the admissible extension as well as about their particular cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-24T13:58:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special cases",
      "compatible topologies",
      "admissible extension",
      "meager sets",
      "baire property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}