{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T05:12:49Z","timestamp":1743052369366,"version":"3.40.3"},"publisher-location":"New York, NY","reference-count":36,"publisher":"Springer New York","isbn-type":[{"type":"print","value":"9781461472537"},{"type":"electronic","value":"9781461472544"}],"license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-1-4614-7254-4_24","type":"book-chapter","created":{"date-parts":[[2013,8,1]],"date-time":"2013-08-01T18:35:43Z","timestamp":1375382143000},"page":"419-425","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Set Theory: Geometric and Real"],"prefix":"10.1007","author":[{"given":"P\u00e9ter","family":"Komj\u00e1th","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,5,18]]},"reference":[{"key":"24_CR1","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/BF02762863","volume":"39","author":"U. Abraham","year":"1981","unstructured":"U. Abraham: Free sets for nowhere-dense set mappings, Israel Journal of Mathematics, 39 (1981), 167\u2013176.","journal-title":"Israel Journal of Mathematics"},{"key":"24_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1307\/mmj\/1029001004","volume":"20","author":"F. Bagemihl","year":"1973","unstructured":"F. Bagemihl: The existence of an everywhere dense independent set, Michigan Mathematical Journal\n                20 (1973), 1\u20132.","journal-title":"Michigan Mathematical Journal"},{"key":"24_CR3","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/0097-3165(75)90016-3","volume":"18","author":"J. E.Baumgartner","year":"1975","unstructured":"J. E.Baumgartner: Partitioning vector spaces, J. Comb. Theory, Ser. A.\n                18 (1975),231\u2013233.","journal-title":"J. Comb. Theory, Ser. A."},{"key":"24_CR4","first-page":"1247","volume":"14","author":"J. Ceder","year":"1969","unstructured":"J. Ceder: Finite subsets and countable decompositions of Euclidean spaces, Rev. Roumaine Math. Pures Appl.\n                14 (1969), 1247\u20131251.","journal-title":"Rev. Roumaine Math. Pures Appl."},{"key":"24_CR5","unstructured":"Z. Dar\u00f3czy: Jelent\u00e9s az 1965. \u00e9vi Schweitzer Mikl\u00f3s matematikai\u00a0eml\u00e9kversenyr\u0151l, Matematikai Lapok\n                17 (1966), 344\u2013366. (in Hungarian)"},{"key":"24_CR6","first-page":"343","volume":"38","author":"R. O. Davies","year":"1963","unstructured":"R. O. Davies: Covering the plane with denumerably many curves, Bull. London Math. Soc.\n                38 (1963), 343\u2013348.","journal-title":"Bull. London Math. Soc."},{"key":"24_CR7","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1017\/S0305004100046983","volume":"72","author":"R. O. Davies","year":"1972","unstructured":"R. O. Davies: Partitioning the plane into denumerably many sets without repeated distances, Proc. Camb. Phil. Soc.\n                72 (1972), 179\u2013183.","journal-title":"Proc. Camb. Phil. Soc."},{"key":"24_CR8","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1112\/blms\/6.2.189","volume":"6","author":"R. O. Davies","year":"1974","unstructured":"R. O. Davies: Covering the space with denumerably many curves, Bull. London Math. Soc.\n                6 (1974), 189\u2013190.","journal-title":"Bull. London Math. Soc."},{"key":"24_CR9","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1090\/S0002-9939-1950-0035809-8","volume":"1","author":"P. Erd\u0151s","year":"1950","unstructured":"P. Erd\u0151s: Some remarks on set theory, Proc. Amer. Math. Soc.\n                1 (1950), 127\u2013141.","journal-title":"Proc. Amer. Math. Soc."},{"issue":"\u201354","key":"24_CR10","first-page":"51","volume":"2","author":"P. Erd\u0151s","year":"1953","unstructured":"P. Erd\u0151s: Some remarks on set theory, III, Michigan Mathematical Journal\n                2 (1953\u201354), 51\u201357.","journal-title":"Michigan Mathematical Journal"},{"issue":"\u201354","key":"24_CR11","first-page":"169","volume":"2","author":"P. Erd\u0151s","year":"1953","unstructured":"P. Erd\u0151s: Some remarks on set theory IV, Mich. Math.\n                2 (1953\u201354), 169\u2013173.","journal-title":"Mich. Math."},{"key":"24_CR12","unstructured":"P. Erd\u0151s: Hilbert terben lev\u0151 ponthalmazok n\u00e9h\u00e1ny geometriai \u00e9s halmazelm\u00e9leti tulajdons\u00e1g\u00e1r\u00f3l, Matematikai Lapok\n                19 (1968), 255\u2013258 (Geometrical and set theoretical properties of subsets of Hilbert spaces, in Hungarian)."},{"issue":"\u201379","key":"24_CR13","doi-asserted-by":"crossref","first-page":"113","DOI":"10.2307\/44151159","volume":"4","author":"P. Erd\u0151s","year":"1978","unstructured":"P. Erd\u0151s: Set-theoretic, measure-theoretic, combinatorial, and number-theoretic problems concerning point sets in Euclidean space, Real Anal. Exchange\n                4 (1978\u201379), 113\u2013138.","journal-title":"Real Anal. Exchange"},{"key":"24_CR14","unstructured":"P. Erd\u0151s: My Scottish Book \u201cProblems\u201d, in: The Scottish Book, Mathematics from the Scottish Caf\u00e9 (ed. R.D.Mauldin), Birkhauser, 1981,35\u201343."},{"key":"24_CR15","unstructured":"P. Erd\u0151s, R. L. Graham, P. Montgomery, B. L. Rothschild, J. Spencer, E. G. Straus: Euclidean Ramsey theorems II, in: Infinite and Finite Sets, Keszthely (Hungary), 1973, ColI. Math. Soc. J. Bolyai 10, 529\u2013557."},{"key":"24_CR16","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1307\/mmj\/1028998389","volume":"7","author":"P. Erd\u0151s","year":"1960","unstructured":"P. Erd\u0151s, A. Hajnal: Some remarks on set theory, VIII, Michigan Mathematical Journal\n                7 (1960), 187\u2013191.","journal-title":"Michigan Mathematical Journal"},{"key":"24_CR17","first-page":"101","volume":"145","author":"P. Erd\u0151s","year":"1994","unstructured":"P. Erd\u0151s, S. Jackson, R. D. Mauldin: On partitions of lines and space, Fund. Math.\n                145 (1994), 101\u2013119.","journal-title":"Fund. Math."},{"key":"24_CR18","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1090\/S0002-9904-1943-07954-2","volume":"49","author":"P. Erd\u0151s","year":"1943","unstructured":"P. Erd\u0151s, S. Kakutani: On non-denumerable graphs, Bull. Amer. Math. Soc., 49 (1943), 457\u2013461.","journal-title":"Bull. Amer. Math. Soc."},{"key":"24_CR19","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF02187793","volume":"5","author":"P. Erd\u0151s","year":"1990","unstructured":"P. Erd\u0151s, P. Komj\u00e1th: Countable decompositions of R\n                2 and R\n                3, Discrete and Computational Geometry\n                5 (1990), 325\u2013331.","journal-title":"Discrete and Computational Geometry"},{"key":"24_CR20","doi-asserted-by":"crossref","first-page":"190","DOI":"10.2307\/2273955","volume":"51","author":"C. Freiling","year":"1986","unstructured":"C. Freiling: Axioms of symmetry: Throwing darts at the real number line, Journal of Symbolic Logic\n                51 (1986), 190\u2013200.","journal-title":"Journal of Symbolic Logic"},{"key":"24_CR21","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1215\/ijm\/1256047607","volume":"24","author":"H. Friedman","year":"1980","unstructured":"H. Friedman: A consistent Fubini-Tonelli theorem for nonmeasurable functions, Illinois Journal of Mathematics, 24 (1980), 390\u2013395.","journal-title":"Illinois Journal of Mathematics"},{"key":"24_CR22","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/BF02789314","volume":"11","author":"S. H. Hechler","year":"1972","unstructured":"S. H. Hechler: Directed graphs over topological spaces: some set theoretical aspects, Israel Journal of Mathematics\n                11 (1972), 231\u2013248.","journal-title":"Israel Journal of Mathematics"},{"key":"24_CR23","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1112\/blms\/23.2.116","volume":"23","author":"P. Komj\u00e1th","year":"1991","unstructured":"P. Komj\u00e1th: Tetrahedron free decomposition of R\n                3, Bull. London Math. Soc.\n                23 (1991), 116\u2013120.","journal-title":"Bull. London Math. Soc."},{"key":"24_CR24","first-page":"181","volume":"14","author":"P. Komj\u00e1th","year":"1992","unstructured":"P. Komj\u00e1th: The master coloring, Comptes Rendus Math\u00e9matiques de l\u2019Academie des sciences, la Soci\u00e9t\u00e9 royale du Canada, 14(1992), 181\u2013182.","journal-title":"Comptes Rendus Math\u00e9matiques de l\u2019Academie des sciences, la Soci\u00e9t\u00e9 royale du Canada"},{"key":"24_CR25","doi-asserted-by":"crossref","unstructured":"P. Komj\u00e1th: Set theoretic constructions in Euclidean spaces, in : New trends in Discrete and Computational Geometry, (J. Pach, ed.), Springer, Algorithms and Combinatorics, 10 (1993), 303\u2013325.","DOI":"10.1007\/978-3-642-58043-7_13"},{"key":"24_CR26","doi-asserted-by":"crossref","unstructured":"P. Komj\u00e1th: A decomposition theorem for R\n                \n                  n\n                , Proc. Amer. Math. Soc.\n                120 (1994), 921\u2013927.","DOI":"10.1090\/S0002-9939-1994-1169038-0"},{"key":"24_CR27","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF01876338","volume":"28","author":"P. Komj\u00e1th","year":"1994","unstructured":"P. Komj\u00e1th: Partitions of vector spaces, Periodica Math. Hung.\n                28 (1994), 187\u2013193.","journal-title":"Periodica Math. Hung."},{"key":"24_CR28","unstructured":"P. Komj\u00e1th: A note on set mappings with meager images, Studia Math. Hung., accepted."},{"key":"24_CR29","doi-asserted-by":"crossref","unstructured":"K. Kunen: Partitioning Euclidean space, Math. Proc. Camb. Phil. Soc.\n                102, (1987), 379\u2013383.","DOI":"10.1017\/S0305004100067426"},{"key":"24_CR30","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1090\/S0002-9939-1987-0884475-3","volume":"100","author":"L. Newelski","year":"1987","unstructured":"L. Newelski, J. Pawlikowski, W. Seredy\u0144iski: Infinite free set for small measure set mappings, Proc. Amer. Math. Soc.\n                100 (1987), 335\u2013339.","journal-title":"Proc. Amer. Math. Soc."},{"key":"24_CR31","unstructured":"J. H. Schmerl: Partitioning Euclidean space, Discrete and Computational Geometry"},{"key":"24_CR32","unstructured":"J. H. Schmerl: Triangle-free partitions of Euclidean space, to appear."},{"key":"24_CR33","unstructured":"J. H. Schmerl: Countable partitions of Euclidean space, to appear."},{"key":"24_CR34","unstructured":"W. Sierpi\u0144iski: Sur un th\u00e9or\u00e8ms \u00e9quivalent \u00e0 l\u2019hypothese du continu, Bull. Int. Acad. Sci. Cracovie A (1919), 1\u20133."},{"key":"24_CR35","unstructured":"W. Sierpi\u0144iski: Hypoth\u00e8se du continu, Warsaw, 1934."},{"key":"24_CR36","first-page":"69","volume":"65","author":"J. C. Simms","year":"1991","unstructured":"J. C. Simms: Sierpi\u0144iski\u2019s theorem, Simon Stevin\n                65 (1991), 69\u2013163.","journal-title":"Simon Stevin"}],"container-title":["The Mathematics of Paul Erd\u0151s II"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4614-7254-4_24","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T12:56:34Z","timestamp":1674132994000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-1-4614-7254-4_24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9781461472537","9781461472544"],"references-count":36,"URL":"https:\/\/doi.org\/10.1007\/978-1-4614-7254-4_24","relation":{},"subject":[],"published":{"date-parts":[[2013]]},"assertion":[{"value":"18 May 2013","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}