{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T14:24:22Z","timestamp":1648909462479},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,7]]},"abstract":"<jats:p> We prove that, for a connected linearly ordered space L, the following conditions are equivalent: (1) L satisfies Sarkovski\u012d's Theorem, (2) there exist turbulent functions on L, and (3) there exists a compact subspace of L which satisfies Sarkovski\u012d's Theorem. Our results are applied in two ways. Firstly, we show that there exist connected linearly ordered spaces without infinite minimal sets; secondly, for each cardinal number \u03bb of uncountable cofinality, we construct a connected linearly ordered space L such that: (1) L is a compact nonfirst countable space satisfying Sarkovski\u012d's Theorem, (2) L admits a dense first countable subset, and (3) the density of L is \u03bb. <\/jats:p>","DOI":"10.1142\/s0218127403007515","type":"journal-article","created":{"date-parts":[[2003,8,28]],"date-time":"2003-08-28T05:49:31Z","timestamp":1062049771000},"page":"1665-1671","source":"Crossref","is-referenced-by-count":2,"title":["A Note on  Sarkovski\u012d's Theorem in Connected Linearly Ordered Spaces"],"prefix":"10.1142","volume":"13","author":[{"given":"D.","family":"Alcaraz","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica, Universidad Polit\u00e9cnica de Cartagena, C\/Doctor Fleming, s\/n, Cartagena, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Sanchis","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Jaume I, Campus del Riu Sec s\/n, 12071, Castell\u00f3, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"1","author":"Alcaraz D.","journal-title":"Rend. Istit. Mat. Univ. Trieste"},{"key":"rf2","first-page":"39","volume":"17","author":"Baldwin S.","journal-title":"Houston J. Math."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0084762"},{"key":"rf4","volume-title":"Recent Progress in General Topolofy","author":"de Vries J.","year":"1992"},{"key":"rf5","volume-title":"General Topology","author":"Engelking R.","year":"1977"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-7819-2"},{"key":"rf7","volume-title":"Topology","author":"Hocking L. G.","year":"1961"},{"key":"rf8","volume-title":"Surveys in General Topology","author":"Lutzer D. J.","year":"1980"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.2307\/2975290"},{"key":"rf10","first-page":"61","volume":"16","author":"Sarkovski\u012d A. N.","journal-title":"Ukrain. Math. Zh."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02527365"},{"key":"rf12","first-page":"385","volume":"11","author":"Schirmer H.","journal-title":"Houston J. Math."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01614086"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403007515","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:16:24Z","timestamp":1565122584000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403007515"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7]]},"references-count":13,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,7]]}},"alternative-id":["10.1142\/S0218127403007515"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403007515","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,7]]}}}