{
  "id": "0809.4187",
  "version": "v1",
  "published": "2008-09-24T18:54:56.000Z",
  "updated": "2008-09-24T18:54:56.000Z",
  "title": "Coinductive properties of Lipschitz functions on streams",
  "authors": [
    "Jiho Kim"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A simple hierarchical structure is imposed on the set of Lipschitz functions on streams (i.e. sequences over a fixed alphabet set) under the standard metric. We prove that sets of non-expanding and contractive functions are closed under a certain coiterative construction. The closure property is used to construct new final stream coalgebras over finite alphabets. For an example, we show that the 2-adic extension of the Collatz function and certain variants yield final bitstream coalgebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-24T18:54:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B99",
      "68Q70"
    ],
    "keywords": [
      "lipschitz functions",
      "coinductive properties",
      "variants yield final bitstream coalgebras",
      "final stream coalgebras",
      "fixed alphabet set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4187K"
    }
  }
}