{
  "id": "1710.00640",
  "version": "v1",
  "published": "2017-09-21T22:26:38.000Z",
  "updated": "2017-09-21T22:26:38.000Z",
  "title": "On the Global Continuity of the Roots of Families of Monic Polynomials (in Russian)",
  "authors": [
    "Evgeny E. Bukzhalev"
  ],
  "comment": "12 pages, in Russian",
  "categories": [
    "math.CA"
  ],
  "abstract": "We raise a question on the existence of continuous roots of families of monic polynomials (by the root of a family of polynomials we mean a function of the coefficients of polynomials of a given family that maps each tuple of coefficients to a root of the polynomial with these coefficients). We prove that the family of monic second-degree polynomials with complex coefficients and the families of monic fourth-degree and fifth-degree polynomials with real coefficients have no continuous root. We also prove that the family of monic second-degree polynomials with real coefficients has continuous roots and we describe the set of all such roots.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-21T22:26:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12Y99"
    ],
    "keywords": [
      "monic polynomials",
      "global continuity",
      "monic second-degree polynomials",
      "continuous root",
      "real coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "ru",
      "license": "arXiv",
      "status": "editable"
    }
  }
}