{
  "id": "1411.3173",
  "version": "v1",
  "published": "2014-11-12T13:42:44.000Z",
  "updated": "2014-11-12T13:42:44.000Z",
  "title": "On $α$-embedded subsets of products",
  "authors": [
    "Olena Karlova",
    "Volodymyr Mykhaylyuk"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We prove that every continuous function $f:E\\to Y$ depends on countably many coordinates, if $E$ is an $(\\aleph_1,\\aleph_0)$-invariant pseudo-$\\aleph_1$-compact subspace of a product of topological spaces and $Y$ is a space with a regular $G_\\delta$-diagonal. Using this fact for any $\\alpha<\\omega_1$ we construct an $(\\alpha+1)$-embedded subspace of a completely regular space which is not $\\alpha$-embedded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-12T13:42:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54B10",
      "54C45",
      "54C20",
      "54H05"
    ],
    "keywords": [
      "embedded subsets",
      "regular space",
      "compact subspace",
      "coordinates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.3173K"
    }
  }
}