{
  "id": "2003.07744",
  "version": "v1",
  "published": "2020-03-17T14:24:34.000Z",
  "updated": "2020-03-17T14:24:34.000Z",
  "title": "Homotopy properties of the space $OS_{f}(X)$",
  "authors": [
    "Kh. ~Kh. ~Kurbanov",
    "A. ~Ya. ~Ishmetov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "For a given compact Hausdorff space $X$, we construct the space $OS_{f}(X)$ of normed, order-preserving, weakly additive, positively homogeneous and semi-additive functionals (for brevity, semi-additive functionals) and it is proved that the hyperspace $\\exp\\, X$ of the space $X$ is a deformation retract of the constructed space. Further we show that the shapes of the spaces $OS_{f}(X)$ and $\\exp\\, X$ coincide. We establish that if the space $\\exp\\, X$ is contractible, then the space $OS_{f}(X)$ is also contractible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-17T14:24:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C65",
      "52A30"
    ],
    "keywords": [
      "homotopy properties",
      "semi-additive functionals",
      "compact hausdorff space",
      "deformation retract"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}