{"paper":{"title":"Shift-preserving maps on $\\omega^*$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Will Brian","submitted_at":"2016-05-04T19:13:00Z","abstract_excerpt":"The shift map $\\sigma$ on $\\omega^*$ is the continuous self-map of $\\omega^*$ induced by the function $n \\mapsto n+1$ on $\\omega$. Given a compact Hausdorff space $X$ and a continuous function $f: X \\rightarrow X$, we say that $(X,f)$ is a quotient of $(\\omega^*,\\sigma)$ whenever there is a continuous surjection $Q: \\omega^* \\to X$ such that $Q \\circ \\sigma = f \\circ Q$.\n  Our main theorem states that if the weight of $X$ is at most $\\aleph_1$, then $(X,f)$ is a quotient of $(\\omega^*,\\sigma)$ if and only if $f$ is weakly incompressible (which means that no nontrivial open $U \\subseteq X$ has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01385","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":""},"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"}