{
  "id": "1509.04985",
  "version": "v1",
  "published": "2015-09-16T18:02:12.000Z",
  "updated": "2015-09-16T18:02:12.000Z",
  "title": "Self-maps under the compact-open topology",
  "authors": [
    "Richard Lupton",
    "Max F. Pitz"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "This paper investigates the space $C_k(\\omega^*,\\omega^*)$, the space of continuous self-maps on the Stone-\\v{C}ech remainder of the integers, $\\omega^*$, equipped with the compact-open topology. Our main results are that (1) $C_k(\\omega^*,\\omega^*)$ is Baire, (2) Stone-\\v{C}ech extensions of injective maps on $\\omega$ form a dense set of weak $P$-points in $C_k(\\omega^*,\\omega^*)$, (3) it is independent of ZFC whether $C_k(\\omega^*,\\omega^*)$ contains $P$-points, and that (4) $C_k(\\omega^*,\\omega^*)$ is not an $F$-space, but contains, as $\\omega^*$, no non-trivial convergent sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-16T18:02:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54D35",
      "54G05",
      "54E52"
    ],
    "keywords": [
      "compact-open topology",
      "non-trivial convergent sequences",
      "main results",
      "dense set",
      "extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}