{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T08:08:40Z","timestamp":1648627720180},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5398,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1999,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>To any metric space it is possible to associate the cardinal invariant corresponding to the least number of rectifiable curves in the space whose union is not meagre. It is shown that this invariant can vary with the metric space considered, even when restricted to the class of convex subspaces of separable Banach spaces. As a corollary it is obtained that it is consistent with set theory that any set of reals of size \u2135<jats:sub>1<\/jats:sub> is meagre yet there are \u2135<jats:sub>1<\/jats:sub> rectifiable curves in \u211d<jats:sup>3<\/jats:sup> whose union is not meagre. The consistency of this statement when the phrase \u201crectifiable curves\u201d is replaced by \u201cstraight lines\u201d remains open.<\/jats:p>","DOI":"10.2307\/2586494","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T14:03:01Z","timestamp":1146924181000},"page":"701-726","source":"Crossref","is-referenced-by-count":2,"title":["Unions of rectifiable curves in Euclidean space and the covering number of the meagre ideal"],"prefix":"10.1017","volume":"64","author":[{"given":"Juris","family":"Stepr\u0101ns","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200013566_ref012","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/19.4.305"},{"key":"S0022481200013566_ref010","first-page":"185","article-title":"Almost disjoint families of lattice paths","volume":"16","author":"Stepr\u0101ns","year":"1991","journal-title":"Topology Proceedings"},{"key":"S0022481200013566_ref009","volume-title":"Transactions of the American Mathematical Society","author":"Stepr\u0101ns"},{"key":"S0022481200013566_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9754-0_20"},{"key":"S0022481200013566_ref007","first-page":"183","volume-title":"Proceedings of the AMS-IMS-S1AM joint summer research conference held in Boulder, Colorado, June 19\u201325, 1983","volume":"31","author":"Shelah","year":"1984"},{"key":"S0022481200013566_ref006","doi-asserted-by":"publisher","DOI":"10.4064\/cm-53-1-133-135"},{"key":"S0022481200013566_ref004","unstructured":"Miller A. , Questions 1996, see http:\/\/www.math.ufl.edu\/\u02dclogic\/."},{"key":"S0022481200013566_ref003","doi-asserted-by":"publisher","DOI":"10.2307\/2044851"},{"key":"S0022481200013566_ref011","first-page":"157","volume-title":"Proceeding of the BEST conferences 1\u20133","volume":"192","author":"Stepr\u0101ns","year":"1995"},{"key":"S0022481200013566_ref001","doi-asserted-by":"publisher","DOI":"10.1201\/9781439863466"},{"key":"S0022481200013566_ref002","first-page":"42","volume":"58","author":"Cichon","year":"1993","journal-title":"Combinatorial properties of the ideal"},{"key":"S0022481200013566_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/cm-48-2-261-264"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200013566","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T17:17:35Z","timestamp":1557422255000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200013566\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1999,6]]}},"alternative-id":["S0022481200013566"],"URL":"https:\/\/doi.org\/10.2307\/2586494","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}