{
  "id": "2104.14612",
  "version": "v1",
  "published": "2021-04-29T18:59:26.000Z",
  "updated": "2021-04-29T18:59:26.000Z",
  "title": "Browder's Theorem with General Parameter Space",
  "authors": [
    "Eilon Solan",
    "Omri Nisan Solan"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "Browder (1960) proved that for every continuous function $F : X \\times Y \\to Y$, where $X$ is the unit interval and $Y$ is a nonempty, convex, and compact subset of $\\dR^n$, the set of fixed points of $F$, defined by $C_F := \\{ (x,y) \\in X \\times Y \\colon F(x,y)=y\\}$ has a connected component whose projection to the first coordinate is $X$. We extend this result to the case where $X$ is a connected and compact Hausdorff space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-29T18:59:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55M20"
    ],
    "keywords": [
      "general parameter space",
      "browders theorem",
      "compact hausdorff space",
      "first coordinate",
      "unit interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}