{
  "id": "2403.04276",
  "version": "v1",
  "published": "2024-03-07T07:19:55.000Z",
  "updated": "2024-03-07T07:19:55.000Z",
  "title": "Certain observations on selection principles related to bornological covers using ideals",
  "authors": [
    "D. Chandra",
    "P. Das",
    "S. Das"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We study selection principles related to bornological covers using the notion of ideals. We consider ideals $\\mathcal I$ and $\\mathcal J$ on $\\omega$ and standard ideal orderings $KB, K$. Relations between cardinality of a base of a bornology with certain selection principles related to bornological covers are established using cardinal invariants such as modified pseudointersection number, the unbounding number and slaloms numbers. When $\\mathcal I \\leq_\\square \\mathcal J$ for ideals $\\mathcal I, \\mathcal J$ and $\\square\\in \\{1\\text{-}1,KB,K\\}$, implications among various selection principles related to bornological covers are established. Under the assumption that ideal $\\mathcal I$ has a pseudounion we show equivalences among certain selection principles related to bornological covers. Finally, the $\\mathcal I\\text{-}\\mathfrak B^s$-Hurewicz property of $X$ is investigated. We prove that $\\mathcal I\\text{-}\\mathfrak B^s$-Hurewicz property of $X$ coincides with the $\\mathfrak B^s$-Hurewicz property of $X$ if $\\mathcal I$ has a pseudounion. Implications or equivalences among selection principles, games and $\\mathcal I\\text{-}\\mathfrak B^s$-Hurewicz property which are obtained from our investigations are described in diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-07T07:19:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "54C35",
      "54A25"
    ],
    "keywords": [
      "bornological covers",
      "hurewicz property",
      "observations",
      "standard ideal orderings",
      "study selection principles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}