{
  "id": "2309.13491",
  "version": "v1",
  "published": "2023-09-23T22:55:45.000Z",
  "updated": "2023-09-23T22:55:45.000Z",
  "title": "Extension properties of orbit spaces for proper actions revisited",
  "authors": [
    "Sergey A. Antonyan"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2308.12237",
  "categories": [
    "math.GN",
    "math.GT"
  ],
  "abstract": "Let $G$ be a locally compact Hausdorff group. We study orbit spaces of equivariant absolute neighborhood extensors ($G$-${\\rm ANE}$'s) for the class of all proper $G$-spaces that are metrizable by a $G$-invariant metric. We prove that if a $G$-space $X$ is a $G$-${\\rm ANE}$ and all $G $-orbits in $X$ are metrizable, then the $G$-orbit space $X/G$ is an {\\rm ANE}. If $G$ is either a Lie group or an almost connected group, then for any closed normal subgroup $H$ of $G$, the $H$-orbit space $X/H$ is a $G/H$-{\\rm ANE} provided that all $H$-orbits in $X$ are metrizable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-23T22:55:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C55",
      "54C20",
      "54H15",
      "57S20"
    ],
    "keywords": [
      "proper actions",
      "extension properties",
      "equivariant absolute neighborhood extensors",
      "study orbit spaces",
      "locally compact hausdorff group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}