{
  "id": "1302.2935",
  "version": "v4",
  "published": "2013-02-12T22:05:34.000Z",
  "updated": "2015-09-16T19:36:47.000Z",
  "title": "The D-topology for diffeological spaces",
  "authors": [
    "J. Daniel Christensen",
    "Gord Sinnamon",
    "Enxin Wu"
  ],
  "comment": "v1: 13 pages; v2: 19 pages, includes proofs of conjectures from v1; v3: 18 pages, minor improvements to exposition; v4: 18 pages, minor corrections",
  "journal": "Pacific Journal of Mathematics 272(1) (2014), 87-110",
  "doi": "10.2140/pjm.2014.272.87",
  "categories": [
    "math.DG"
  ],
  "abstract": "Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural topology called the $D$-topology. However, the $D$-topology has not yet been studied seriously in the existing literature. In this paper, we develop the basic theory of the $D$-topology for diffeological spaces. We explain that the topological spaces that arise as the $D$-topology of a diffeological space are exactly the $\\Delta$-generated spaces and give results and examples which help to determine when a space is $\\Delta$-generated. Our most substantial results show how the $D$-topology on the function space $C^{\\infty}(M,N)$ between smooth manifolds compares to other well-known topologies.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-03-10T19:01:55.000Z",
      "comment": "v1: 13 pages; v2: 19 pages, includes proofs of conjectures from v1; v3: 18 pages, minor improvements to exposition",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-09-16T19:36:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57P99",
      "58D99",
      "57R99"
    ],
    "keywords": [
      "diffeological space",
      "d-topology",
      "function space",
      "smooth manifolds compares",
      "well-known topologies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.2935C"
    }
  }
}