{"paper":{"title":"Autohomeomorphisms of pre-images of $\\mathbb N^*$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Alan Dow","submitted_at":"2024-06-13T16:56:07Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09319","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.09319/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}