{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T20:27:59Z","timestamp":1761596879980,"version":"3.41.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2004,11,16]],"date-time":"2004-11-16T00:00:00Z","timestamp":1100563200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2004,12]]},"abstract":"<jats:p>Every compact metric space <jats:inline-formula>$X$<\/jats:inline-formula> is homeomorphically embedded in an <jats:inline-formula>$\\omega$<\/jats:inline-formula>-algebraic domain <jats:inline-formula>$D$<\/jats:inline-formula> as the set of minimal limit (that is, non-finite) elements. Moreover, <jats:inline-formula>$X$<\/jats:inline-formula> is a retract of the set <jats:inline-formula>$L(D)$<\/jats:inline-formula> of all limit elements of <jats:inline-formula>$D$<\/jats:inline-formula>. Such a domain <jats:inline-formula>$D$<\/jats:inline-formula> can be chosen so that it has property M and finite-branching, and the height of <jats:inline-formula>$L(D)$<\/jats:inline-formula> is equal to the small inductive dimension of <jats:inline-formula>$X$<\/jats:inline-formula>. We also show that the small inductive dimension of <jats:inline-formula>$L(D)$<\/jats:inline-formula> as a topological space is equal to the height of <jats:inline-formula>$L(D)$<\/jats:inline-formula> for domains with property M. These results give a characterisation of the dimension of a space <jats:inline-formula>$X$<\/jats:inline-formula> as the minimal height of <jats:inline-formula>$L(D)$<\/jats:inline-formula> in which <jats:inline-formula>$X$<\/jats:inline-formula> is embedded as the set of minimal elements. The domain in which we embed an <jats:inline-formula>$n$<\/jats:inline-formula>-dimensional compact metric space <jats:inline-formula>$X$<\/jats:inline-formula> (<jats:inline-formula>$n \\leq \\infinity$<\/jats:inline-formula>) has a concrete structure in that it consists of finite\/infinite sequences in <jats:inline-formula>$\\{0,1,\\bot\\}$<\/jats:inline-formula> with at most <jats:inline-formula>$n$<\/jats:inline-formula> copies of <jats:inline-formula>$\\bot$<\/jats:inline-formula>.<\/jats:p>","DOI":"10.1017\/s0960129504004396","type":"journal-article","created":{"date-parts":[[2004,11,16]],"date-time":"2004-11-16T15:28:09Z","timestamp":1100618889000},"page":"853-878","source":"Crossref","is-referenced-by-count":4,"title":["Compact metric spaces as minimal-limit sets in domains of bottomed sequences"],"prefix":"10.1017","volume":"14","author":[{"given":"HIDEKI","family":"TSUIKI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2004,11,16]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129504004396","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T19:13:43Z","timestamp":1750446823000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129504004396\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,11,16]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2004,12]]}},"alternative-id":["S0960129504004396"],"URL":"https:\/\/doi.org\/10.1017\/s0960129504004396","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"type":"print","value":"0960-1295"},{"type":"electronic","value":"1469-8072"}],"subject":[],"published":{"date-parts":[[2004,11,16]]}}}