{
  "id": "1710.07854",
  "version": "v1",
  "published": "2017-10-21T21:35:49.000Z",
  "updated": "2017-10-21T21:35:49.000Z",
  "title": "Group structures of a function spaces with the set-open topology",
  "authors": [
    "Alexander V. Osipov"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GN",
    "math.AT",
    "math.GR",
    "math.RA"
  ],
  "abstract": "In this paper, we find at the properties of the family lambda which imply that the function space C(X,R^alpha) with the lambda-open topology is a semitopological group (paratopological group, topological group, topological vector space and other algebraic structures) under the usual operations of addition and multiplication (and multiplication by scalars).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-21T21:35:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function space",
      "group structures",
      "set-open topology",
      "lambda-open topology",
      "topological vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}