{
  "id": "1210.8074",
  "version": "v2",
  "published": "2012-10-30T16:35:19.000Z",
  "updated": "2013-08-07T18:10:53.000Z",
  "title": "One-point extensions and local topological properties",
  "authors": [
    "M. R. Koushesh"
  ],
  "comment": "4 pages",
  "journal": "Bull. Aust. Math. Soc. 88 (2013), 12-16",
  "categories": [
    "math.GN"
  ],
  "abstract": "A space $Y$ is called an extension of a space $X$ if $Y$ contains $X$ as a dense subspace. An extension $Y$ of $X$ is called a one-point extension of $X$ if $Y\\backslash X$ is a singleton. P. Alexandroff proved that any locally compact non-compact Hausdorff space $X$ has a one-point compact Hausdorff extension, called the one-point compactification of $X$. Motivated by this, S. Mr\\'{o}wka and J.H. Tsai [On local topological properties. II, Bull. Acad. Polon. Sci. S\\'{e}r. Sci. Math. Astronom. Phys. 19 (1971), 1035-1040] posed the following more general question: For what pairs of topological properties ${\\mathscr P}$ and ${\\mathscr Q}$ does a locally-${\\mathscr P}$ space $X$ having ${\\mathscr Q}$ possess a one-point extension having both ${\\mathscr P}$ and ${\\mathscr Q}$? Here, we provide an answer to this old question.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-07T18:10:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D35"
    ],
    "keywords": [
      "local topological properties",
      "one-point extension",
      "locally compact non-compact hausdorff space",
      "one-point compact hausdorff extension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.8074K"
    }
  }
}