{"paper":{"title":"Minimality, distality and equicontinuity for semigroup actions on compact Hausdorff spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joseph Auslander, Xiongping Dai","submitted_at":"2017-08-03T04:38:20Z","abstract_excerpt":"Let $\\pi\\colon T\\times X\\rightarrow X$ with phase map $(t,x)\\mapsto tx$, denoted $(\\pi,T,X)$, be a \\textit{semiflow} on a compact Hausdorff space $X$ with phase semigroup $T$. If each $t\\in T$ is onto, $(\\pi,T,X)$ is called surjective; and if each $t\\in T$ is 1-1 onto $(\\pi,T,X)$ is called invertible and in latter case it induces $\\pi^{-1}\\colon X\\times T\\rightarrow X$ by $(x,t)\\mapsto xt:=t^{-1}x$, denoted $(\\pi^{-1},X,T)$. In this paper, we show that $(\\pi,T,X)$ is equicontinuous surjective iff it is uniformly distal iff $(\\pi^{-1},X,T)$ is equicontinuous surjective. As applications of this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00996","kind":"arxiv","version":9},"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"}