{
  "id": "1608.03685",
  "version": "v1",
  "published": "2016-08-12T06:16:48.000Z",
  "updated": "2016-08-12T06:16:48.000Z",
  "title": "Separable determination in Banach spaces",
  "authors": [
    "Marek Cuth"
  ],
  "comment": "The content of Section 3 (concerning separable determination of generalized lushness) was previously contained in a preprint with the title \"Separable determination of (generalized-)lushness\". The paper \"Separable determination of (generalized-)lushness\" was withdrawn from arxiv, because it is not intended for publication as its content is covered here",
  "categories": [
    "math.FA",
    "math.GN"
  ],
  "abstract": "We study a relation between three different formulations of theorems on separable determination - one using the concept of rich families, second via the concept of suitable models and third, a new one, suggested in this paper, using the notion of $\\omega$-monotone mappings. In particular, we show that in Banach spaces all those formulations are in a sense equivalent and we give a positive answer to two questions of O. Kalenda and the author. Our results enable us to obtain new statements concerning separable determination of $\\sigma$-porosity (and of similar notions) in the language of rich families; thus, not using any terminology from logic or set theory. Moreover, we prove that in Asplund spaces, generalized lushness is separably determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-12T06:16:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B26",
      "46B20",
      "03C30"
    ],
    "keywords": [
      "banach spaces",
      "rich families",
      "set theory",
      "formulations",
      "similar notions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}