{
  "id": "1802.08117",
  "version": "v1",
  "published": "2018-02-22T15:56:39.000Z",
  "updated": "2018-02-22T15:56:39.000Z",
  "title": "Topological spaces of persistence modules and their properties",
  "authors": [
    "Peter Bubenik",
    "Tane Vergili"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AT",
    "math.GN"
  ],
  "abstract": "Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules, including many of those that have been previously studied, and describe the relationships between them. In the cases where these classes are sets, interleaving distance induces a topology. We undertake a systematic study the resulting topological spaces and their basic topological properties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-22T15:56:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N99",
      "54A05",
      "18A25"
    ],
    "keywords": [
      "persistence modules",
      "topological spaces",
      "natural way",
      "central algebraic object arising",
      "systematic study"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}