{
  "id": "1002.3089",
  "version": "v1",
  "published": "2010-02-16T14:47:14.000Z",
  "updated": "2010-02-16T14:47:14.000Z",
  "title": "Group topologies coarser than the Isbell topology",
  "authors": [
    "S. Dolecki",
    "F. Jordan",
    "F. Mynard"
  ],
  "journal": "Topology and its Applications, 158(15): 1962-1968, 2011",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "The Isbell, compact-open and point-open topologies on the set $C(X,\\mathbb{R})$ of continuous real-valued maps can be represented as the dual topologies with respect to some collections $\\alpha(X)$ of compact families of open subsets of a topological space $X$. Those $\\alpha(X)$ for which addition is jointly continuous at the zero function in $C_\\alpha(X,\\mathbb{R})$ are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections $\\alpha(X)$ for which $C_{\\alpha}(X,\\mathbb{R})$ is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if $X$ is infraconsonant. Examples based on measure theoretic methods, that $C_\\alpha (X,\\mathbb{R})$ can be strictly finer than the compact-open topology, are given. To our knowledge, this is the first example of a splitting group topology strictly finer than the compact-open topology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-16T14:47:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "54C40",
      "54A10"
    ],
    "keywords": [
      "group topologies coarser",
      "compact-open topology",
      "measure theoretic methods",
      "vector space topology",
      "splitting group topology strictly finer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.3089D"
    }
  }
}