{
  "id": "1006.4405",
  "version": "v1",
  "published": "2010-06-23T02:12:18.000Z",
  "updated": "2010-06-23T02:12:18.000Z",
  "title": "Characterization of $\\ell_p$-like and $c_0$-like equivalence relations",
  "authors": [
    "Longyun Ding"
  ],
  "comment": "8 pages, submitted",
  "categories": [
    "math.LO",
    "math.GN"
  ],
  "abstract": "Let $X$ be a Polish space, $d$ a pseudo-metric on $X$. If $\\{(u,v):d(u,v)<\\delta\\}$ is ${\\bf\\Pi}^1_1$ for each $\\delta>0$, we show that either $(X,d)$ is separable or there are $\\delta>0$ and a perfect set $C\\subseteq X$ such that $d(u,v)\\ge\\delta$ for distinct $u,v\\in C$. Granting this dichotomy, we characterize the positions of $\\ell_p$-like and $c_0$-like equivalence relations in the Borel reducibility hierarchy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-23T02:12:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "54E35",
      "46A46"
    ],
    "keywords": [
      "equivalence relations",
      "characterization",
      "borel reducibility hierarchy",
      "perfect set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.4405D"
    }
  }
}