{
  "id": "2203.09045",
  "version": "v1",
  "published": "2022-03-17T02:52:53.000Z",
  "updated": "2022-03-17T02:52:53.000Z",
  "title": "Construction of nearly pseudocompactification",
  "authors": [
    "Biswajit Mitra",
    "Sanjib Das"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "A space is nearly pseudocompact if and only if $\\upsilon X\\backslash X$ is dense in $\\beta X\\backslash X$. If we denote $K=cl_{\\beta X}(\\upsilon X\\backslash X)$, then $\\delta X=X\\cup(\\beta X\\backslash K)$ is referred by Henriksen and Rayburn \\cite{hr80} as nearly pseudocompact extension of $X$. Henriksen and Rayburn studied the nearly pseudocompact extension using different properties of $\\beta X$. In this paper our main motivation is to construct nearly pseudocompact extension of $X$ independently and not using any kind of extension property of $\\beta X$. An alternative construction of $\\beta X$ is made by taking the family of all $z$-ultrafilters on $X$ and then topologized in a suitable way. In this paper we also adopted the similar idea of constructing the $\\delta X$ from the scratch, taking the collection of all $z$-ultrafilters on $X$ of some kind, called $hz$-ultrafilters, together with fixed $z$-ultrafilter and then be topologized in the similar way what we do in the construction of $\\beta X.$ We have further shown that the extension $\\delta X$ is unique with respect to certain properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-17T02:52:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudocompact extension",
      "ultrafilter",
      "pseudocompactification",
      "similar way",
      "main motivation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}