{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T03:46:20Z","timestamp":1648957580454},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2008,5,17]],"date-time":"2008-05-17T00:00:00Z","timestamp":1210982400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2008,12]]},"DOI":"10.1007\/s00454-008-9079-5","type":"journal-article","created":{"date-parts":[[2008,5,16]],"date-time":"2008-05-16T14:30:04Z","timestamp":1210948204000},"page":"481-503","source":"Crossref","is-referenced-by-count":0,"title":["On the Number of Topological Types Occurring in a Parameterized Family of Arrangements"],"prefix":"10.1007","volume":"40","author":[{"given":"Saugata","family":"Basu","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,5,17]]},"reference":[{"key":"9079_CR1","series-title":"Handbook of Computational Geometry","first-page":"49","volume-title":"Arrangements and Their Applications","author":"P.K. Agarwal","year":"2000","unstructured":"Agarwal, P.K., Sharir, M.: In: Urrutia, J., Sack, J.R. (eds.) Arrangements and Their Applications. Handbook of Computational Geometry, pp. 49\u2013119. North-Holland, Amsterdam (2000). MR 1746675"},{"key":"9079_CR2","doi-asserted-by":"crossref","unstructured":"Basu, S.: Combinatorial complexity in o-minimal geometry. Preprint at arXiv:math.CO\/0612050 (2006). An extended abstract appears in the Proceedings of the ACM Symposium on the Theory of Computing (2007)","DOI":"10.1145\/1250790.1250798"},{"key":"9079_CR3","first-page":"139","volume-title":"Algorithmic Semi-algebraic Geometry and Topology\u2014Recent Progress and Open Problems. Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics","author":"S. Basu","year":"2008","unstructured":"Basu, S.: Algorithmic Semi-algebraic Geometry and Topology\u2014Recent Progress and Open Problems. Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics, vol.\u00a0453, pp.\u00a0139\u2013212. American Mathematical Society, Providence (2008)"},{"issue":"3","key":"9079_CR4","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1112\/jlms\/jdm069","volume":"76","author":"S. Basu","year":"2007","unstructured":"Basu, S., Vorobjov, N.: On the number of homotopy types of fibres of a definable map. J. Lond. Math. Soc. (2) 76(3), 757\u2013776 (2007). MR 2377123","journal-title":"J. Lond. Math. Soc. (2)"},{"key":"9079_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-33099-2","volume-title":"Algorithms in Real Algebraic Geometry, Algorithms and Computation in Mathematics","author":"S. Basu","year":"2006","unstructured":"Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry, Algorithms and Computation in Mathematics, 2nd edn., vol.\u00a010. Springer, Berlin (2006). MR 1998147 (2004g:14064)","edition":"2"},{"key":"9079_CR6","unstructured":"Coste, M.: An introduction to o-minimal geometry. Istituti Editoriali e Poligrafici Internazionali, Pisa, Dip. Mat. Univ. Pisa, Dottorato di Ricerca in Matematica (2000)"},{"key":"9079_CR7","series-title":"Proc. Sympos. Pure Math.","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1090\/pspum\/007\/0157289","volume-title":"Helly\u2019s Theorem and Its Relatives","author":"L. Danzer","year":"1963","unstructured":"Danzer, L., Gr\u00fcnbaum, B., Klee, V.: Helly\u2019s Theorem and Its Relatives. Proc. Sympos. Pure Math., vol.\u00a0VII, pp.\u00a0101\u2013180. Am. Math. Soc., Providence (1963). MR 0157289 (28 #524)"},{"key":"9079_CR8","volume-title":"A History of Algebraic and Differential Topology. 1900\u20131960","author":"J. Dieudonn\u00e9","year":"1989","unstructured":"Dieudonn\u00e9, J.: A History of Algebraic and Differential Topology. 1900\u20131960. Birkh\u00e4user Boston, Boston (1989). MR 995842 (90g:01029)"},{"key":"9079_CR9","unstructured":"Gabrielov, A., Vorobjov, N.: Approximation of definable sets by compact families and upper bounds on homotopy and homology. Preprint at arXiv:math.AG\/0710.3028v1 (2007)"},{"issue":"1\u20132","key":"9079_CR10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0747-7171(88)80005-1","volume":"5","author":"D.Yu. Grigor\u2019ev","year":"1988","unstructured":"Grigor\u2019ev, D.Yu., Vorobjov, N.N. Jr.: Solving systems of polynomial inequalities in subexponential time. J. Symb. Comput. 5(1\u20132), 37\u201364 (1988). MR 949112 (89h:13001)","journal-title":"J. Symb. Comput."},{"issue":"2","key":"9079_CR11","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1090\/S0002-9947-1986-0833698-1","volume":"295","author":"J.F. Knight","year":"1986","unstructured":"Knight, J.F., Pillay, A., Steinhorn, C.: Definable sets in ordered structures. II. Trans. Am. Math. Soc. 295(2), 593\u2013605 (1986). MR 0833698 (88b:03050b)","journal-title":"Trans. Am. Math. Soc."},{"key":"9079_CR12","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0039-7","volume-title":"Lectures on Discrete Geometry","author":"J. Matou\u0161ek","year":"2002","unstructured":"Matou\u0161ek, J.: Lectures on Discrete Geometry. Graduate Texts in Mathematics, vol.\u00a0212, Springer, New York (2002). MR 1899299 (2003f:52011)"},{"issue":"2","key":"9079_CR13","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1090\/S0002-9947-1986-0833697-X","volume":"295","author":"A. Pillay","year":"1986","unstructured":"Pillay, A., Steinhorn, C.: Definable sets in ordered structures. I. Trans. Am. Math. Soc. 295(2), 565\u2013592 (1986). MR 0833697 (88b:03050a)","journal-title":"Trans. Am. Math. Soc."},{"issue":"2","key":"9079_CR14","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1090\/S0002-9947-1988-0943306-9","volume":"309","author":"A. Pillay","year":"1988","unstructured":"Pillay, A., Steinhorn, C.: Definable sets in ordered structures. III. Trans. Am. Math. Soc. 309(2), 469\u2013576 (1988). MR 0943306 (89i:03059)","journal-title":"Trans. Am. Math. Soc."},{"issue":"4","key":"9079_CR15","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1090\/S0894-0347-03-00427-2","volume":"16","author":"J.-P. Rolin","year":"2003","unstructured":"Rolin, J.-P., Speissegger, P., Wilkie, A.J.: Quasianalytic Denjoy-Carleman classes and o-minimality. J. Am. Math. Soc. 16(4), 751\u2013777 (2003), (electronic). MR 1992825 (2004g:14065)","journal-title":"J. Am. Math. Soc."},{"key":"9079_CR16","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1090\/S0002-9939-1957-0087106-9","volume":"8","author":"S. Smale","year":"1957","unstructured":"Smale, S.: A Vietoris mapping theorem for homotopy. Proc. Am. Math. Soc. 8, 604\u2013610 (1957). MR 0087106 (19,302f)","journal-title":"Proc. Am. Math. Soc."},{"key":"9079_CR17","volume-title":"Algebraic Topology","author":"E.H. Spanier","year":"1966","unstructured":"Spanier, E.H.: Algebraic Topology. McGraw\u2013Hill, New York (1966). MR 0210112 (35 #1007)"},{"key":"9079_CR18","doi-asserted-by":"crossref","first-page":"203","DOI":"10.2307\/1970004","volume":"67","author":"E.H. Spanier","year":"1958","unstructured":"Spanier, E.H., Whitehead, J.H.C.: Duality in relative homotopy theory. Ann. Math. (2) 67, 203\u2013238 (1958). MR 0105105 (21 #3850)","journal-title":"Ann. Math. (2)"},{"key":"9079_CR19","series-title":"Stud. Logic Found. Math.","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/S0049-237X(08)71811-1","volume-title":"Remarks on Tarski\u2019s Problem Concerning (R,+,\u22c5,exp)","author":"L. Dries van den","year":"1984","unstructured":"van den Dries, L.: Remarks on Tarski\u2019s Problem Concerning (R,+,\u22c5,exp), Logic Colloquium \u201982, Florence, 1982. Stud. Logic Found. Math., vol.\u00a0112, pp.\u00a097\u2013121. North-Holland, Amsterdam (1984). MR 762106 (86g:03052)"},{"key":"9079_CR20","series-title":"London Mathematical Society Lecture Note Series","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511525919","volume-title":"Tame Topology and O-Minimal Structures","author":"L. Dries van den","year":"1998","unstructured":"van den Dries, L.: Tame Topology and O-Minimal Structures. London Mathematical Society Lecture Note Series, vol.\u00a0248. Cambridge University Press, Cambridge (1998). MR 1633348 (99j:03001)"},{"issue":"2","key":"9079_CR21","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1215\/S0012-7094-96-08416-1","volume":"84","author":"L. Dries van den","year":"1996","unstructured":"van den Dries, L., Miller, C.: Geometric categories and o-minimal structures. Duke Math. J. 84(2), 497\u2013540 (1996). MR 1404337 (97i:32008)","journal-title":"Duke Math. J."},{"issue":"11","key":"9079_CR22","doi-asserted-by":"crossref","first-page":"4377","DOI":"10.1090\/S0002-9947-98-02105-9","volume":"350","author":"L. Dries van den","year":"1998","unstructured":"van den Dries, L., Speissegger, P.: The real field with convergent generalized power series. Trans. Am. Math. Soc. 350(11), 4377\u20134421 (1998). MR 1458313 (99a:03036)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"9079_CR23","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1112\/S0024611500012648","volume":"81","author":"L. Dries van den","year":"2000","unstructured":"van den Dries, L., Speissegger, P.: The field of reals with multisummable series and the exponential function. Proc. Lond. Math. Soc. (3) 81(3), 513\u2013565 (2000). MR 1781147 (2002k:03057)","journal-title":"Proc. Lond. Math. Soc. (3)"},{"key":"9079_CR24","series-title":"Topology. II, Encyclopaedia Math. Sci.","volume-title":"Homology and Cohomology","author":"O.Ya. Viro","year":"2004","unstructured":"Viro, O.Ya., Fuchs, D.B.: Homology and Cohomology. Topology. II, Encyclopaedia Math. Sci., vol.\u00a024. Springer, Berlin (2004). Translated from the Russian by C.J. Shaddock, pp. 95\u2013196. MR 2054457"},{"key":"9079_CR25","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6318-0","volume-title":"Elements of Homotopy Theory","author":"G.W. Whitehead","year":"1978","unstructured":"Whitehead, G.W.: Elements of Homotopy Theory. Graduate Texts in Mathematics, vol.\u00a061. Springer, New York (1978). MR 516508 (80b:55001)"},{"issue":"4","key":"9079_CR26","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1090\/S0894-0347-96-00216-0","volume":"9","author":"A.J. Wilkie","year":"1996","unstructured":"Wilkie, A.J.: Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function. J. Am. Math. Soc. 9(4), 1051\u20131094 (1996). MR 1398816 (98j:03052)","journal-title":"J. Am. Math. Soc."},{"issue":"4","key":"9079_CR27","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s000290050052","volume":"5","author":"A.J. Wilkie","year":"1999","unstructured":"Wilkie, A.J.: A theorem of the complement and some new o-minimal structures. Selecta Math. (N.S.) 5(4), 397\u2013421 (1999). MR 1740677 (2001c:03071)","journal-title":"Selecta Math. (N.S.)"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9079-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-008-9079-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9079-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,5]],"date-time":"2020-05-05T19:20:39Z","timestamp":1588706439000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-008-9079-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5,17]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["9079"],"URL":"https:\/\/doi.org\/10.1007\/s00454-008-9079-5","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5,17]]}}}