{
  "id": "1205.6966",
  "version": "v1",
  "published": "2012-05-31T12:20:37.000Z",
  "updated": "2012-05-31T12:20:37.000Z",
  "title": "One-point extensions of locally compact paracompact spaces",
  "authors": [
    "M. R. Koushesh"
  ],
  "comment": "22 pages",
  "journal": "Bull. Iranian Math. Soc. 37 (2011), no. 4, 199-228",
  "categories": [
    "math.GN"
  ],
  "abstract": "A space $Y$ is called an {\\em extension} of a space $X$ if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {\\em equivalent} if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Y\\leq Y'$ if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ of $X$ is called a {\\em one-point extension} if $Y\\backslash X$ is a singleton. An extension $Y$ of $X$ is called {\\em first-countable} if $Y$ is first-countable at points of $Y\\backslash X$. Let ${\\mathcal P}$ be a topological property. An extension $Y$ of $X$ is called a {\\em ${\\mathcal P}$-extension} if it has ${\\mathcal P}$. In this article, for a given locally compact paracompact space $X$, we consider the two classes of one-point \\v{C}ech-complete ${\\mathcal P}$-extensions of $X$ and one-point first-countable locally-${\\mathcal P}$ extensions of $X$, and we study their order-structures, by relating them to the topology of a certain subspace of the outgrowth $\\beta X\\backslash X$. Here ${\\mathcal P}$ is subject to some requirements and include $\\sigma$-compactness and the Lindel\\\"{o}f property as special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-31T12:20:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "54D35",
      "54D40",
      "54D45",
      "54E50"
    ],
    "keywords": [
      "locally compact paracompact space",
      "one-point extension",
      "dense subspace",
      "special cases",
      "equivalence classes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.6966K"
    }
  }
}