81. ANTYKWARIAT VIVARIUM - Ksi±¿ki 92. Pól wieku matematyki polskiej 19201970 (kazimierz kuratowski). 93. Pólwieku matematyki polskiej 1920-1970 (kazimierz kuratowski). 94. http://www.vivarium.com.pl/sklep/index.php?SessID=&mode=1&kategoria=10

82. W£ADYS£AW ORLICZ (1903-1990) Orlicz continued his studies by attending lectures on mathematics given at the GeneralFaculty of Lvov Polytechnic, where he listened to kazimierz kuratowski. http://www.wmid.amu.edu.pl/en/wyklady/orlicz/orlicz.html

W£ADYS£AW ORLICZ (1903-1990) by Lech Maligranda (Lulea), Witold Wnuk (Poznañ) Childhood and early adolescence Studies and the beginnings of scholarly career The Thirtieths - beginnings of fame The years of World War II ... Childhood and early adolescence W³adys³aw Roman Orlicz was born in Okocim on Sunday, 24 May 1903. He was the third child of Franciszek and Maria Orlicz who raised five sons: Kazimierz, Tadeusz, W³adys³aw, Zbigniew and Micha³. The fourth brother was killed in action during the struggles for Poland’s eastern frontiers in 1918 – 1920 while the oldest died before the end of World War II, his health damaged by incarceration in the concentration camp at Stutthof. Of the remaining three all became professors of natural or technical sciences: Tadeusz was a specialist in wood technology while Micha³ busied himself with climatology and meteorology. Studies and the beginnings of scholarly career W³adys³aw Orlicz began professional work already during his studies. Since 1923 he had served as a demonstrator in the Chair of Mathematics of the Faculty of Philosophy at the Jan Kazimierz University. On 1 August 1925, he was appointed a teaching fellow at the First Chair of Mathematics. The completion of studies in the 1925/26 academic year coincided with his first publication devoted to the theory of summability. The paper appeared in the Tohoku Mathematical Journal in 1926. W³adys³aw Orlicz continued his studies by attending lectures on mathematics given at the General Faculty of Lvov Polytechnic, where he listened to Kazimierz Kuratowski.

83. Mathematicians During The Third Reich And World War II 1952 dismissed for a second time. kuratowski, kazimierz Risked his life toteach in illegal educational establishment through the war in Poalnd. http://wwwzenger.informatik.tu-muenchen.de/~huckle/mathwar.html

Mathematicians during the Third Reich and World War II Prof. Thomas Huckle huckle@in.tum.de Last modified: March/12/2004 Died Imprisoned Hidden Emigration ... General Information Died: Berwald, Ludwig: Dismissed 1939 in Prague; Deportation by Gestapo to Lodz where he died in April 1942. Blumenthal, Otto: [SCHAPPACHER, SIEGMUND,PINL] dismissed 1939 from Aachen and - for a short while - kept in "protective custody". Editor of 'Mathematische Annalen' until 1938. In 1939 he went to Holland. When the Netherlands had fallen, he refused the help of Dutch friends and was deported to Theresienstadt where he died 1944. Cavailles, Jean: [MENZLER-TROTT] Member of the resistance. Killed by the Gestapo 1944. See also Dickstein, Samuel: Died in the Nazi bombing of Warsaw in 1939. Epstein, Paul: [SIEGMUND, PINL] Frankfurt 1919 until 1935, suicide after summon from Gestapo August 1939. Froehlich, Walter: In 1939 dismissed in Prague, 1941 deported to Lodz and died there 1942. Hartogs, Fritz

84. Short Biography Of Stefan Banach By Waclaw Szybalski And Stanislaw Kosiedowski service, was about to take up a post at the Jan kazimierz University in Lwów. whoalso fed lice in Lwów in 194144; se below) , kuratowski, Mazurkiewicz, and http://wwwzenger.informatik.tu-muenchen.de/~huckle/szyb.htm

Short biography of Stefan Banach with correcting the entry in the St. Andrews biography by Waclaw Szybalski and Stanislaw Kosiedowski Born: 30 March 1892 in Kraków, Austria-Hungary (now Poland) Died: 31 Aug 1945 in Lwów, Soviet-occupied Eastern Poland, that in 1945 was in the process of ethnic cleansing (deportation) of Polish population by the Soviet authorities (now Lviv, Ukraine). His grave is shown in this picture http://republika.pl/polskilwow/banach.jpg Banach's father had never given his son much support, but now once he left school he quite openly told Banach that he was now on his own. Banach left Kraków and went to Lwów where he enrolled in the Faculty of Engineering at Lwów Technical University (Politechnika Lwowska). It is almost certain that Banach, without any financial support, had to support himself by tutoring. This must have occupied quite a lot of his time and when he graduated in 1914 he had taken longer to complete the course than was normal. He had returned to Kraków frequently during the period of his studies in Lwów from 1910 to 1914. It is not entirely clear what Banach's plans were in 1914 but the outbreak of World War I in August, shortly after his graduation, saw Banach leave Lwów. At the time Banach studied there, Lwów was, a under Austrian control as it had been from the partition of Poland in 1772. In Banach's youth the polish Poland, in some sense, existed only under Austian occupation in Kraków and in Lwów, but did not exist and Russia-controlled much of the country. Warsaw only had a Russian language university and was situated in what was named "Vistula Land". With the outbreak of World War I, the Russian troops occupied the city of Lwów. Banach was not physically fit for army service, having poor vision in his left eye. During the war he worked building roads but also spent time in Kraków where he earned money by teaching in the local schools. He also attended mathematics lectures at the Jagiellonian University in Kraków and, although this is not completely certain, it is believed that he attended Zaremba's lectures.

85. Stanislaw M. Ulam Papers, 1916-1984 George Bogdan), 1900; kuratowski, kazimierz, 1896-; Lomnicki, ZbigniewA. Mandelbrot, Benoit B. Mazur, Stanislaw; Metropolis, N. (Nicholas http://www.amphilsoc.org/library/mole/u/ulam.htm

Stanislaw M. Ulam Papers (36 linear feet) Ms. Coll. 54 American Philosophical Society 105 South Fifth Street * Philadelphia, PA 19106-3386 Table of contents Abstract A gifted mathematician, Polish-born Stanislaw Ulam made contributions to set theory, topology, mathematical logic, and number theory, but is most widely remembered for his work in fostering the technical development of thermonuclear weapons. He was associated with Los Alamos Scientific Laboratories for most of the years between 1943 and 1965, and thereafter with the University of Colorado. These papers include personal and professional correspondence, manuscripts of both published and unpublished works, and memorabilia. Background note Scope and content Administrative information Restrictions on use ... Series XV. Miscellaneous reprints, manuscripts, and journals, 1938-1986 Return to MOLE: APS Manuscripts On-Line Return to APS Library Return to APS home Background note Stanislaw Ulam Stanislaw Ulam was gifted mathematician who, during the course of his career, made significant contributions to set theory, topology, ergodic theory, probability, cellular automata theory, the study of nonlinear processes, the function of real variables, mathematical logic, and number theory. Perhaps his greatest achievement was the development of the Monte Carlo method for solving complex mathematical problems by electronic random sampling, but he made equally noteworthy contributions in hydrodynamics (three-dimensional fluid flow), the development of nuclear propulsion for space flight (Project Orion), and in fields as disparate as physics, biology, and astronomy. Yet despite the breadth of his scholarship, Ulam is most often remembered for the central role he played in the early development of the American hydrogen bomb.

86. File 22-1-95.TXT Dateilänge 46 KB * * * * Bearbeiter N. BRENTON(003) 24 RUSSELL,BERTRAND(005) 25 kuratowski,kazimierz(005) 25 SPR http://www.phil.uni-passau.de/dlwg/ws03/22-1-95.txt

ERLÄUTERUNGEN ZU DEN LITERATURHINWEISEN: 1. FORMALBIBLIOGRAPHISCHE INFORMATIONEN V - Verfasser TI - Titel (hinter "..." evtl. ein Abstract) Z - Zeitschriften-(Festschrift usw.) Titel BD - Band (mögliche Abkürzungen: "S" f. Sonderheft, "J" f. Jahrbuch JG - Jahrgang SE - Seiten DT - Dokumententyp (mögliche Abkürzung: "JO" f. Zeitschrift, "CO" f. Kongressakte, "HO" f. Festschrft, "RE" f. Reader SPR - Sprache des Artikels (mögliche Abkürzungen: die ersten vier Buchstaben der englischen Bezeichnung der Sprache, also z.B. "GERM" für deutsch). 2. INHALTLICHE INFORMATION Eine inhaltliche Erschliessung der Nachweise wurde erreicht durch 1. eine Anzahl dem Text entnommener Sachwörter oder Namen (als sogenannte "Deskriptoren"), 2. die Kennzeichnung des thematischen Zusammenhangs der Deskriptoren, 3. die Angabe der Wichtigkeit der Deskriptoren im vorliegenden Dokument In (035)/Kant, Immanuel (020)/Lorentz, Hendrik Antoon (035) SPR: GERM (freie Naturgesetz (035)/Erfahrung (035)/Deskript.) Relativitätstheorie

87. List Of Mathematical Topics (J-L) - Wikipedia, The Free Encyclopedia Ktheory Kullback-Leibler divergence Kummer Kummer, Ernst Kummer, ErnstEduard Kummer theory kuratowski, kazimierz kuratowski closure http://en.wikipedia.org/wiki/List_of_mathematical_topics_(J-L)

List of mathematical topics (J-L) From Wikipedia, the free encyclopedia. List of mathematical topics A-C D-F G-I J-L M-O P-R S-U V-Z ... edit J J-invariant Jacobi, Carl Gustav Jakob Jacobi identity Jacobi's elliptic functions ... edit K K-Hyperperfect number K-fold perfect number Kac Kac, Mark ... edit L L-function L-system La Géometrie Lafforgue ... LZW Views Article Discussion Edit History Personal tools Log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Special pages This page was last modified 17:22, 30 May 2004. All text is available under the terms of the GNU Free Documentation License (see for details). About Wikipedia

88. Planar Graph - Wikipedia, The Free Encyclopedia The Polish mathematician kazimierz kuratowski provided a characterization of planargraphs, now known as kuratowski s theorem A finite graph is planar if and http://en.wikipedia.org/wiki/Planar_graph

Planar graph From Wikipedia, the free encyclopedia. In graph theory , a planar graph is a graph that can be embedded in a plane so that no edges intersect. For example, the following two graphs are planar: (the second one can be redrawn without intersecting edges by moving one of the diagonal edges to the outside), while the two graphs shown below are not planar: It is not possible to redraw these without edge intersections. In fact, these two are the smallest non-planar graphs, a consequence of the characterization below. The Polish mathematician Kazimierz Kuratowski provided a characterization of planar graphs, now known as Kuratowski's theorem A finite graph is planar if and only if it does not contain a subgraph that is an expansion of K (the complete graph on 5 vertices) or K complete bipartite graph on six vertices, three of which connect to each of the other three). An expansion of a graph results from inserting vertices into edges, i.e. changing an edge * - * to * - * - *, and repeating this zero or more times. Equivalent formulations of this theorem include A finite graph is planar if and only if it does not contain a subgraph that is homeomorphic to K or K and A finite graph is planar if and only if it does not have K or K as a minor A far-reaching generalization of Kuratowski's theorem is given by the Robertson-Seymour theorem ; in the language of this theorem

89. Metamath Proof Explorer - Df-op Wiener gave the first successful definition 1 , justified by opthwiener 1750, whichwas simplified by kazimierz kuratowski in 1921 to our present definition. http://us.metamath.org/mpegif/df-op.html

Home Metamath Proof Explorer Browser slow? Try the Unicode version Definition df-op Description: Kuratowski's ordered pair definition. Definition 9.1 of [ Quine ] p. 58. For proper classes it is not meaningful but is well-defined and we allow it for convenience. For the justifying theorem (for sets) see opth . There are other ways to define ordered pairs; the basic requirement is that two ordered pairs are equal iff their respective members are equal. In 1914 Norbert Wiener gave the first successful definition , justified by opthwiener , which was simplified by Kazimierz Kuratowski in 1921 to our present definition. An even simpler definition is justified by opthreg , but it requires the Axiom of Regularity for its justification and is not commonly used. A definition that also works for proper classes is , justified by opthprc . If we restrict our sets to nonnegative integers, an ordered pair definition that involves only elementary arithmetic is provided by . Finally, an ordered pair of real numbers can be represented by a complex number as shown by

90. Encyclopedia4U - List Of Mathematical Topics (J-L) - Encyclopedia Article Kruskal, Martin Kruskal s algorithm Ktheory Kummer Kummer, Ernst Kummer, Ernst Eduard kuratowski, kazimierz kuratowski closure axioms http://www.encyclopedia4u.com/l/list-of-mathematical-topics-j-l-.html

ENCYCLOPEDIA U com Lists of articles by category ... Encyclopedia Home Page SEARCH : List of mathematical topics (J-L) A-C D-F G-I - J-L - M-O P-R S-U V-Z J Jacobi, Carl Gustav Jakob Jacobi identity Jacobian Jacobian matrix ... Johnson solid Jones, Vaughan Frederick Randal Jordan, Camille Jordan curve theorem Jordan normal form Josephus permutation ... Julia Sets K K-Hyperperfect number K-fold perfect number Kac Kac, Mark Kaiser window Kanada, Yasumasa Kantorovich, Leonid Vitalyevich Karnaugh map Kastner, Abraham Gotthelf KdV equation Kêng-Chih, Tsu Kepler, Johannes Kepler's laws of planetary motion Kepler solid Kernel (algebra) ... Koch snowflake Kodaira, Kunihiko Kolmogorov, Andrey Nikolaevich Kolmogorov-Arnold-Moser theorem Kolmogorov Smirnov test Kolmogorov space ... Kontsevich, Maxim Korteweg, Diederik Kovalevskaya, Sofia Kovalevskaya, Sofia Vasilyevna Kowa, Seki Kramp, Christian Kronecker, Leopold Krull dimension Kruskal, Martin Kruskal's algorithm K-theory Kummer Kummer, Ernst Kummer, Ernst Eduard Kuratowski, Kazimierz Kuratowski closure axioms ... Kurtosis Kutta, Martin Wilhelm L L-function L-system Lafforgue Lafforgue, Laurent

91. Mostra Eventos Da Data Selecionada Translate this page do reinado de Teodor Andrzej Potocki - Polônia 02/02/1896 Nascimento MatemáticaFatos Polônia Nascimento de kazimierz kuratowski (matemático polonês) 04/02 http://www.ponteiro.com.br/mostrad9.php?w=29

92. The Mathematics Genealogy Project - Update Data For Kazimierz Kuratowski The Mathematics Genealogy Project http://www.genealogy.ams.org/html/php/submit-update.php?id=24546

93. SmartPedia.com - Free Online Encyclopedia - Encyclopedia Books. Bartel. kazimierz Funk, kazimierz II Sprawiedliwy, kazimierz IV. kazimierzKuratowski, kazimierz Odnowiciel, kazimierz Wielki. kazimierz http://www.smartpedia.com/smart/browse/Special:Allpages&from=Kavango_Region

Search: Math and Natural Sciences Applied Arts Social Sciences Culture ... Interdisciplinary Categories All pages Kavango Region Kavar Kavaslavian Kaveri ... Caption This This document is licensed under the GNU Free Documentation License (GFDL), which means that you can copy and modify it as long as the entire work (including additions) remains under this license. GFDL SOURCE

94. PlanetMath: Kuratowski's Theorem Wagner s theorem is an equivalent later result. References. 1 KazimierzKuratowski. Sur le problème des courbes gauches en topologie. Fund. http://planetmath.org/encyclopedia/KuratowskisTheorem.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List Kuratowski's theorem (Theorem) A finite graph is planar if and only if it contains no subgraph that is isomorphic to or is a subdivision of or , where is the complete graph of order 5 and is the complete bipartite graph with 3 vertices in each of the halfs. Wagner's theorem is an equivalent later result. References Kazimierz Kuratowski. Fund. Math. "Kuratowski's theorem" is owned by bbukh full author list owner history view preamble View style: HTML with images page images TeX source See Also: planar graph Wagner's theorem Keywords: planar Cross-references: equivalent Wagner's theorem vertices complete bipartite graph ... finite There are 2 references to this object. This is version 8 of Kuratowski's theorem , born on 2001-11-12, modified 2004-03-27.

95. AAC Database - Browse - List Translate this page Vergleichende Stadtegeschichte. 1, kuratowski, K. 1, kuratowski, KazimierzSee kuratowski, K. 1, Kurayshi, Rashid. 1, Kurayyim, Karimah. 13, http://valeph.tau.ac.il/ALEPH/ENG/TAU/AAC/AAC/SCAN-F/3074638

Sourasky Central Library Browse - AUTHOR list - ALL DOCUMENTS The numbers in the list below indicate the number of documents listed under a term. To display the documents, click on an eye . To move up or down the list, click on the arrow. Kurat, Akdes Nimet Kuratani, Naoomi Kurath, Gertrude Prokosch Kurath, Hans Kuratorium fur den Aufbau Nationaler Gedenkstatten in Buchenwald, Sachsenhausen, Ravensburg Kuratorium fur Judische Geschichte (Frankfurt am Main, Germany) Kuratorium fur Vergleichende Stadtgeschichte. Institut fur Vergleichende Stadtgeschichte See: Institut fur Vergleichende Stadtegeschichte Kuratowski, K. Kuratowski, Kazimierz See: Kuratowski, K. Kurayshi, Rashid Kurayyim, Karimah Kurbaierische Akademie der Wissenschaften See: Bayerische Akademie der Wissenschaften

96. Biography-center - Letter K Kupka, Frantisek www.artmagick.com/artists/kupka.aspx; kuratowski, Kazimierzwwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/kuratowski.html; http://www.biography-center.com/k.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish K 401 biographies www-history.mcs.st-and.ac.uk/~history/Mathematicians/Konig_Julius.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Konig_Samuel.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Konigsberger.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Kurschak.html Kabir, www.geocities.com/athens/8107/bios1.html#kabir Kac, Mark www-history.mcs.st-and.ac.uk/~history/Mathematicians/Kac.html Kaestner, Abraham www-history.mcs.st-and.ac.uk/~history/Mathematicians/Kaestner.html Kagan, Benjamin www-history.mcs.st-and.ac.uk/~history/Mathematicians/Kagan.html Kahanamoku, Duke Paoa www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=54152 Kahlbaum, Karl Ludwig www.whonamedit.com/doctor.cfm/624.html Kahler, Otto

97. [[enKazimierz Kuratowski]][[plKazimierz Kuratowski]] KazimierzKuratowski (*2. Februar 1896; † 18. Juni 1980 http://www.produkteseite.de/lexikon/artikel-Kazimierz_Kuratowski.html

[[en:Kazimierz Kuratowski]][[pl:Kazimierz Kuratowski]] Kuratowski wurde am [[2. Februar]] [[1896]] in [[Warschau]] geboren. Seine Eltern waren Marek Kuratow, ein Rechtsanwalt, und Rosa von Karzewski. Er schloss [[1913]] das philologische Chrzanowski-Gymnasium in [[Warschau]] ab und ging anschließend ([[1913]]-[[1914]]) nach [[Glasgow]], um dort [[Mathematik]] zu studieren. Nach der Gründung der polnischen Universität in Warschau [[1915]] kehrte er dorthin zurück. [[1918]] schloss er sein Studium an der Warschauer Universität ab und promovierte [[1921]] mit einer zweiteiligen Arbeit, die folgendes umfasste: Doktorvater war Sierpinski; Janiszewski, der offizielle Betreuer, war damals schon nicht mehr am Leben. Als im Februar 1945 die Warschauer Universität wiedereröffnet wurde, nahm er seine Vorlesungstätigkeit wieder auf. Im gleichen Jahr wurde er zum ordentlichen Mitglied der Polnischen Akademie der Wissenschaften berufen, und er war von 1957 bis 1968 ihr Vizepräsident. Unmittelbar nach dem Ende des Zweiten Weltkrieges engagierte er sich aktiv beim Wiederaufbau des wissenschaftlichen Lebens in Polen, indem er unter anderem das Staatliche Mathematische Institut ins Leben rief, das später zum Mathematischen Institut der Polnischen Akademie der Wissenschaften wurde. Er stand diesem Institut 1948-1968 als Direktor vor und war außerdem Vorsitzender des Wissenschaftsrates (1968-1980) und Leiter der Abteilung Topologie (1948-1980). Er nahm aktiv an der Arbeit der Warschauer Wissenschaftlichen Gesellschaft und der Polnischen Mathematischen Gesellschaft teil, war ihr langjähriger Vorsitzender und Ehrenmitglied. Außerdem war er Redakteur der ''"Fundamenta Mathematicae"'', ab 1925 ihr Chefredakteur, des ''"Bulletins der Polnischen Akademie der Wissenschaften"'', Mitschöpfer und Redakteur der Buchreihe ''"Mathematische Monographien"'', in der die wertvollsten Werke der Vertreter der Warschauer und Lwower mathematischen Schule veröffentlicht wurden. Er war Mitglied zahlreicher ausländischer Gesellschaften und Akademien: Der Royal Society of Edinburgh, von Österreich, Deutschland, Ungarn, Italien und der Sowjetunion.

98. Editeur - L'Enseignement Mathematique http://www.math.univ-rennes1.fr/bibli/catalogue/Reference.htm?numrec=19191869191

99. Marmot Library Network /Marmot Mark Year Entries Kuratomi Chizuko 3 Kuratorium Junger Deutscher Film 2003 1 KuratowskiKazimierz 1896 5 Kurcinka Mary Sheedy p1999 1 Kurcinka Mary Sheedy 1953 http://www.millennium.marmot.org:90/kids/1899,2126/search/aKurdin, Igor./akurdin

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