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A definable set <jats:italic>X<\/jats:italic> is of dimension equal to the \u2010dimension of <jats:italic>X<\/jats:italic>. The structure  is simultaneously a first\u2010order topological structure. The dimension rank of a set definable in the first\u2010order topological structure  also coincides with its\u00a0dimension.<\/jats:p>","DOI":"10.1002\/malq.202200069","type":"journal-article","created":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T05:38:48Z","timestamp":1693460328000},"page":"472-481","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pregeometry over locally o\u2010minimal structures and dimension"],"prefix":"10.1002","volume":"69","author":[{"given":"Masato","family":"Fujita","sequence":"first","affiliation":[{"name":"Department of Liberal Arts Japan Coast Guard Academy Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2023,8,30]]},"reference":[{"key":"e_1_2_6_2_1","first-page":"18:1","article-title":"Theories of real addition with and without a predicate for integers","volume":"17","author":"B\u00e8s A.","year":"2021","journal-title":"Logical Methods Comp. 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