{
  "id": "1909.11347",
  "version": "v1",
  "published": "2019-09-25T08:58:25.000Z",
  "updated": "2019-09-25T08:58:25.000Z",
  "title": "A Geometric Vietoris-Begle Theorem, with an Application to Riesz Spaces",
  "authors": [
    "Andrew McLennan"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We show that a surjective map between compact ANR's (absolute neighborhood retracts) is a homotopy equivalence if the fibers are contractible and either the domain is simply connected or the fibers are also ANR's. This is a geometric analogue of the Vietoris-Begle theorem. We use it to show that if $L$ is a locally convex Riesz space, $C \\subset L$ is compact, convex, and metrizable, $x \\in L$, and the function $y \\mapsto x \\vee y$ ($y \\mapsto x \\wedge y$) is continuous, then the image of this map is contractible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-25T08:58:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric vietoris-begle theorem",
      "application",
      "absolute neighborhood retracts",
      "locally convex riesz space",
      "homotopy equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}