{
  "id": "1512.00380",
  "version": "v1",
  "published": "2015-12-01T18:34:38.000Z",
  "updated": "2015-12-01T18:34:38.000Z",
  "title": "Accumulation Points of Graphs of Real Functions",
  "authors": [
    "Balázs Maga"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "During the last few decades E. S. Thomas, S. J. Agronsky, J. G. Ceder, and T. L. Pearson gave an equivalent definition of the real Baire class 1 functions by characterizing their graph. In this paper, using their results, we consider the following problem: let $T$ be a given subset of $[0,1]\\times\\mathbb{R}$. When can we find a function $f:[0,1]\\rightarrow\\mathbb{R}$ such that the accumulation points of its graph are exactly the points of $T$? We show that if such a function exists, we can choose it to be a Baire-2 function. We characterize the accumulation sets of bounded and not necessarily bounded functions separately. We also examine the similar question in the case of Baire-1 functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-01T18:34:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "accumulation points",
      "real functions",
      "real baire class",
      "equivalent definition",
      "pearson gave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}