{"paper":{"title":"$\\mathbb{M}^*$, $\\mathbb{N}^*$, and $\\mathbb{H}^*$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Alan Dow, Klaas Pieter Hart, Will Brian","submitted_at":"2025-05-07T13:58:04Z","abstract_excerpt":"Let $\\mathbb{M} = \\mathbb N \\times [0,1]$. The natural projection $\\pi: \\mathbb{M} \\rightarrow \\mathbb N$, which sends $(n,x)$ to $n$, induces a projection mapping $\\pi^*: \\mathbb{M}^* \\rightarrow \\mathbb N^*$, where $\\mathbb{M}^*$ and $\\mathbb N^*$ denote the \\v{C}ech-Stone remainders of $\\mathbb{M}$ and $\\mathbb N$, respectively.\n  We show that $\\mathsf{CH}$ implies every autohomeomorphism of $\\mathbb N^*$ lifts through the natural projection to an autohomeomorphism of $\\mathbb{M}^*$. That is, for every homeomorphism $h: \\mathbb N^* \\rightarrow \\mathbb N^*$ there is a homeomorphism $H: \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04425","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/2505.04425/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"}