{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:02:18Z","timestamp":1773147738659,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T00:00:00Z","timestamp":1465948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Applying a theorem according to Rhemtulla and Formanek, we partially solve an open problem raised by Hochman with an affirmative answer. Namely, we show that if G is a countable torsion-free locally nilpotent group that acts by homeomorphisms on X, and     S \u2282 G     is a subsemigroup not containing the unit of G such that     f \u2208 \u2329 1 , s f : s \u2208 S \u232a     for every     f \u2208 C ( X )    , then     ( X , G )     has zero topological entropy.<\/jats:p>","DOI":"10.3390\/e18060230","type":"journal-article","created":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T14:11:19Z","timestamp":1465999879000},"page":"230","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Extensions over Semigroups and Applications"],"prefix":"10.3390","volume":"18","author":[{"given":"Wen","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Jin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangdong","family":"Ye","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,6,15]]},"reference":[{"key":"ref_1","first-page":"401","article-title":"The determinism and the Kolmogorov property in topological dynamics","volume":"51","author":"Siemaszko","year":"2003","journal-title":"Bull. 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