{"paper":{"title":"Lowering topological entropy over subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.DS","authors_text":"Guohua Zhang, Wen Huang, Xiangdong Ye","submitted_at":"2008-11-26T06:16:06Z","abstract_excerpt":"Let $(X, T)$ be a topological dynamical system (TDS), and $h (T, K)$ the topological entropy of a subset $K$ of $X$. $(X, T)$ is {\\it lowerable} if for each $0\\le h\\le h (T, X)$ there is a non-empty compact subset with entropy $h$; is {\\it hereditarily lowerable} if each non-empty compact subset is lowerable; is {\\it hereditarily uniformly lowerable} if for each non-empty compact subset $K$ and each $0\\le h\\le h (T, K)$ there is a non-empty compact subset $K_h\\subseteq K$ with $h (T, K_h)= h$ and $K_h$ has at most one limit point.\n  It is shown that each TDS with finite entropy is lowerable, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4230","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"}