{
  "id": "2406.09319",
  "version": "v1",
  "published": "2024-06-13T16:56:07.000Z",
  "updated": "2024-06-13T16:56:07.000Z",
  "title": "Autohomeomorphisms of pre-images of $\\mathbb N^*$",
  "authors": [
    "Alan Dow"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In the study of the Stone-\\u{C}ech remainder of the real line a detailed study of the Stone-\\u{C}ech remainder of the space $\\mathbb N\\times [0,1]$, which we denote as $\\mathbb M$, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to $\\mathbb M$. It is known that an autohomeomorphism of $\\mathbb M^*$ induces an autohomeomorphism of $\\mathbb N^*$. We prove that it is consistent with there being non-trivial autohomeomorphism of $\\mathbb N^*$ that those induced by autohomeomorphisms of $\\mathbb M^*$ are trivial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-13T16:56:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54A35"
    ],
    "keywords": [
      "pre-images",
      "real line",
      "non-trivial autohomeomorphism",
      "closed sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}