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Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.<\/jats:p>","DOI":"10.2307\/2695063","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:05:00Z","timestamp":1146938700000},"page":"1530-1555","source":"Crossref","is-referenced-by-count":15,"title":["Topological elementary equivalence of closed semi-algebraic sets in the real plane"],"prefix":"10.1017","volume":"65","author":[{"given":"Bart","family":"Kuijpers","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Paredaens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Van den Bussche","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011488_ref022","first-page":"17","volume-title":"Proceedings of the 15th ACM symposium on principles of database systems","author":"Stolboushkin","year":"1996"},{"key":"S0022481200011488_ref020","doi-asserted-by":"publisher","DOI":"10.4064\/fm-81-2-159-171"},{"key":"S0022481200011488_ref018","first-page":"763","volume":"52","author":"Pillay","year":"1987","journal-title":"First order topological structures and theories"},{"key":"S0022481200011488_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0097006"},{"key":"S0022481200011488_ref005","first-page":"87","volume-title":"Proceedings of the 16th ACM symposium on principles of database systems","author":"Benedikt","year":"1997"},{"key":"S0022481200011488_ref011","volume-title":"Finite model theory","author":"Ebbinghaus","year":"1995"},{"key":"S0022481200011488_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0062252"},{"key":"S0022481200011488_ref008","doi-asserted-by":"crossref","unstructured":"Collins G. 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