{
  "id": "1903.06459",
  "version": "v1",
  "published": "2019-03-15T11:05:21.000Z",
  "updated": "2019-03-15T11:05:21.000Z",
  "title": "On the duals of normed spaces and quotient shapes",
  "authors": [
    "Nikica Uglesic"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Some properties of the (normed) dual Hom-functor $D$ and its iterations $D^n$ are exhibited. For instance: $D$ turns every canonical embedding (in the second dual space) into a retraction (of the third dual onto the first one); $D$ rises the countably infinite (algebraic) dimension only; $D$ does not change the finite quotient shape type. By means of that, the finite quotient shape classification of normed vectorial spaces is completely solved. As a consequence, two extension type theorems are derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-15T11:05:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normed spaces",
      "finite quotient shape classification",
      "finite quotient shape type",
      "second dual space",
      "extension type theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}