{
  "id": "2412.02209",
  "version": "v1",
  "published": "2024-12-03T06:55:51.000Z",
  "updated": "2024-12-03T06:55:51.000Z",
  "title": "Cardinal Properties of the Space of Quasicontinuous Functions under Topology of Uniform Convergence on Compact Subsets",
  "authors": [
    "Chander Mohan Bishnoi",
    "Sanjay Mishra"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, we investigate various cardinal properties of the space $Q_{C}X$ of all real-valued quasicontinuous functions on the topological space $X$, under the topology of uniform convergence on compact subsets. It begins by examining the relationship between tightness and other properties in the context of the space $X$, highlighting results such as the alignment of tightness $Q_{C}X$ with the compact Lindel\\\"of number of $X$ under Hausdorff conditions and the countable tightness of $Q_{C}X$ when $X$ is second countable. Further investigations reveal conditions for the tightness of $Q_{C}X$ relative to $k$-covers of $X$, as well as connections between density tightness, fan tightness, and other properties in Hausdorff spaces. Additionally, we discuss the implications of the Frechet-Urysohn property $Q_{C}X$ for open $k$-covers in Hausdorff spaces. We explore relationships between $Q_{C}X$'s tightness, the Frechet-Urysohn property, and the $\\sigma$-compactness of locally compact Hausdorff spaces $X$. Furthermore, we examine the $k_{f}$-covering property and the existence of $k$-covers in the context of Whyburn spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-03T06:55:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54A25",
      "54C08",
      "54C30",
      "54D10"
    ],
    "keywords": [
      "cardinal properties",
      "uniform convergence",
      "compact subsets",
      "quasicontinuous functions",
      "frechet-urysohn property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}