{"paper":{"title":"Topology and Topological Sequence Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ruifeng Zhang, \\v{L}ubom\\'ir Snoha, Xiangdong Ye","submitted_at":"2018-10-01T01:02:35Z","abstract_excerpt":"Let $X$ be a compact metric space and $T:X\\longrightarrow X$ be continuous. Let $h^*(T)$ be the supremum of topological sequence entropies of $T$ over all subsequences of $\\mathbb Z_+$ and $S(X)$ be the set of the values $h^*(T)$ for all continuous maps $T$ on $X$. It is known that $\\{0\\} \\subseteq S(X)\\subseteq \\{0, \\log 2, \\log 3, \\ldots\\}\\cup \\{\\infty\\}$. Only three possibilities for $S(X)$ have been observed so far, namely $S(X)=\\{0\\}$, $S(X)=\\{0,\\log2, \\infty\\}$ and $S(X)=\\{0, \\log 2, \\log 3, \\ldots\\}\\cup \\{\\infty\\}$.\n  In this paper we completely solve the problem of finding all possibil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00497","kind":"arxiv","version":2},"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"}