{
  "id": "1508.03778",
  "version": "v1",
  "published": "2015-08-15T23:59:51.000Z",
  "updated": "2015-08-15T23:59:51.000Z",
  "title": "Existence of continuous functions that are one-to-one almost everywhere",
  "authors": [
    "Alexander J. Izzo"
  ],
  "categories": [
    "math.GN",
    "math.PR"
  ],
  "abstract": "It is shown that given a metric space $X$ and a $\\sigma$-finite positive regular Borel measure $\\mu$ on $X$, there exists a bounded continuous real-valued function on $X$ that is one-to-one on the complement of a set of $\\mu$ measure zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-15T23:59:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C30",
      "26E99",
      "46E30",
      "54E40"
    ],
    "keywords": [
      "continuous functions",
      "one-to-one",
      "finite positive regular borel measure",
      "measure zero",
      "metric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803778I"
    }
  }
}