{
  "id": "2211.13266",
  "version": "v1",
  "published": "2022-11-23T19:31:58.000Z",
  "updated": "2022-11-23T19:31:58.000Z",
  "title": "On $κ$-pseudocompactess and uniform homeomorphisms of function spaces",
  "authors": [
    "Mikołaj Krupski"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "A Tychonoff space $X$ is called $\\kappa$-pseudocompact if for every continuous mapping $f$ of $X$ into $\\mathbb{R}^\\kappa$ the image $f(X)$ is compact. This notion generalizes pseudocompactness and gives a stratification of spaces lying between pseudocompact and compact spaces. It is well known that pseudocompactness of $X$ is determined by the uniform structure of the function space $C_p(X)$ of continuous real-valued functions on $X$ endowed with the pointwise topology. In respect of that A.V. Arhangel'skii asked in [Topology Appl., 89 (1998)] if analogous assertion is true for $\\kappa$-pseudocompactness. We provide an affirmative answer to this question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-23T19:31:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54D30",
      "54E15"
    ],
    "keywords": [
      "function space",
      "uniform homeomorphisms",
      "pseudocompactess",
      "notion generalizes pseudocompactness",
      "topology appl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}