33:
530:
1034:
267:
672:
599:
874:
469:(also a future mathematician) spent most of their time working on mathematics problems during breaks and after school. Later in life Banach credited Dr. Kamil Kraft, the mathematics and physics teacher at the school, with kindling his interests in mathematics. While Banach was a diligent student he did, on occasion, receive low grades (he failed Greek during his first semester at the school) and later spoke critically of the school's math teachers.
448:
Puchalska in Kraków. Young Stefan came to regard
Franciszka as his foster mother and Maria as his older sister. In his early years Banach was tutored by Juliusz Mien, a French intellectual and friend of the Płowa family, who had emigrated to Poland and supported himself with photography and translations of Polish literature into French. Mien taught Banach French and most likely encouraged him in his early mathematical pursuits.
570:. Steinhaus became fascinated with the self-taught young mathematician. The encounter resulted in a long-lasting collaboration and friendship. In fact, soon after the encounter Steinhaus invited Banach to solve some problems he had been working on but which had proven difficult. Banach solved them within a week and the two soon published their first joint work (
621:
in 1920 and published in 1922, included the basic ideas of functional analysis, which was soon to become an entirely new branch of mathematics. In his dissertation, written in 1920, he axiomatically defined what is today called a Banach space. The thesis was widely discussed in academic circles and
447:
and as the mother was too poor to support the child, the couple decided that he should be reared by family and friends. Stefan spent the first few years of his life with his grandmother, but when she was taken ill, Greczek arranged for his son to be raised by
Franciszka Płowa and her niece Maria
1620:
655:. First published in Polish in 1931, the next year it was also translated into French and gained wider recognition in European academic circles. The book was also the first in a long series of mathematics monographs edited by Banach and his circle. On 17 June 1924, Banach become a
835:. For a brief period in fact, complete normed linear spaces were referred to as "Banach–Wiener" spaces in mathematical literature, based on terminology introduced by Wiener himself. However, because Wiener's work on the topic was limited, the established name became just
1624:
942:
has been conferred by the Polish
Mathematical Society to mathematicians for best doctoral dissertations in the mathematical sciences with the objective to "promote and financially support the most promising young researchers".
268:
1432:
Stefan Banach (1922). "Sur les opérations dans les ensembles abstraits et leur application aux équations integrals (On operations in the abstract sets and their application to integral equations)".
439:
Unusually, Stefan's surname was his mother's instead of his father's, though he received his father's given name, Stefan. Military regulations did not permit soldiers of Stefan
Greczek's rank to
2061:
1451:
647:, devoted primarily to Banach's field of study—functional analysis. Around that time, Banach also began working on his best-known work, the first monograph on the general theory of
2188:
490:. He initially chose engineering as his field of study since at the time he was convinced that there was nothing new to discover in mathematics. At some point he also attended
494:
in Kraków on a part-time basis. As Banach had to earn money to support his studies it was not until 1914 that he finally, at age 22, passed his high school graduation exams.
741:
Research
Institute. Employment in Weigl's Institute provided many unemployed university professors and their associates protection from random arrest and deportation to
725:
mathematicians, had to promise to learn
Ukrainian to be allowed to keep his chair and continue his academic activities. After the German takeover of Lwów in 1941 during
931:
1544:
2148:
558:, one of the renowned mathematicians of the time. According to Steinhaus, while he was strolling through the gardens he was surprised to overhear the term
2183:
2178:
2083:
1668:
1081:
761:
2198:
1101:
1096:
1646:
1595:
590:. The society was officially founded on 2 April 1919. It was also through Steinhaus that Banach met his future wife, Łucja Braus.
277:
who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern
1212:
32:
984:
celebrated the mathematician's achievements by issuing a series of commemorative coins designed by Robert
Kotowicz (golden 200-
566:
was at the time still a fairly new idea in mathematics) and walked over to investigate. As a result, he met Banach, as well as
2163:
2193:
1868:
1579:
760:
of 1944, Banach returned to the university and helped re-establish it after the war years. However, because the
Soviets were
1548:
1452:"Математичний міст між Краковом і Львовом: як Стефан Банах став одним із найвеличніших математиків століття - krakow1.one"
514:
2013:
1975:
509:
at the local schools, worked in a bookstore and as a foreman of a road building crew. He attended some lectures at the
2143:
505:
opened its offensive toward Lwów, Banach left for Kraków, where he spent the rest of the war. He made his living as a
1956:
1915:
1769:
1742:
1699:
1055:"Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies."
939:
815:, he changed terminology and referred to them as "spaces of type B", which most likely contributed to the subsequent
613:
in 1918, Banach was given an assistantship at the Lwów
Polytechnic. Steinhaus' backing also allowed him to receive a
1716:
2173:
575:
859:
2158:
776:. He was also considered a candidate for Minister of Education of Poland. In January 1945, he was diagnosed with
163:
1894:
1847:
718:
2118:
1946:
1091:
897:
757:
1048:
331:
282:
2203:
641:, soon gave birth to the "Lwów School of Mathematics". In 1929 the group began publishing its own journal,
373:
131:
637:
Young and talented, Banach gathered around him a large group of mathematicians. The group, meeting in the
529:
2168:
927:
851:
587:
501:
broke out, Banach was excused from military service due to his left-handedness and poor vision. When the
313:
139:
416:
family, and was subsequently baptised by his father. Banach's parents were Stefan
Greczek and Katarzyna
1858:
902:
843:
660:
627:
622:
allowed him in 1922 to become a professor at the Lwów Polytechnic. Initially an assistant to Professor
385:
381:
327:
174:
147:
127:
796:
Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of a
1905:
892:
878:
828:
729:, all universities were closed and Banach, along with many colleagues and his son, was employed as a
365:
123:
2074:. Monografie Matematyczne (in French). Vol. 1. Warszawa: Subwencji Funduszu Kultury Narodowej.
1217:
907:
888:
is one of the fundamental theorems of functional analysis. Further theorems related to Banach are:
742:
151:
135:
981:
885:
773:
583:
510:
491:
369:
289:(Theory of Linear Operations), the first monograph on the general theory of functional analysis.
143:
1823:
1207:
1000:
847:
609:
Steinhaus introduced Banach to academic circles and substantially accelerated his career. After
2153:
850:, was included in his dissertation, and was later extended by his students (for example in the
610:
2003:
1003:
on the 100th anniversary of the conversation the two mathematicians held when they first met
797:
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377:
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518:
2138:
2133:
1170:
1076:
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714:
656:
563:
301:
217:
2079:
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and was permitted to stay in Lwów. He died on 31 August 1945, aged 53. His funeral at the
8:
1203:
1086:
935:
919:
863:
804:
800:
278:
111:
487:
323:
2109:
2036:
1883:
1810:
1033:
698:
643:
318:
623:
227:
2009:
1971:
1952:
1911:
1890:
1864:
1843:
1814:
1802:
1765:
1736:
1695:
1575:
1128:
781:
676:
630:. At the same time, from 1922, Banach also headed the second Chair of Mathematics at
626:, in 1927, Banach received his own chair. In 1924 he was accepted as a member of the
335:
671:
237:
2075:
1792:
855:
208:
97:
638:
602:
574:). Steinhaus, Banach and Nikodym, along with several other Kraków mathematicians (
690:
631:
618:
457:
406:
339:
261:
201:
155:
57:
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without actually graduating from a university. The doctoral thesis, accepted by
2023:
1621:"Setna rocznica najsłynniejszej matematycznej dyskusji na krakowskich Plantach"
1059:
1044:
1025:
commemorated the 100th anniversary of Banach receiving his title of professor.
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832:
730:
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361:
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309:
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119:
115:
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1806:
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824:
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stationed in Kraków. Little is known about Banach's mother. According to his
300:
descent, Banach showed a keen interest in mathematics and engaged in solving
274:
159:
81:
2114:
946:
Stefan Banach is the patron of a number of schools and streets including in
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996:
985:
970:
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820:
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710:
706:
702:
652:
648:
598:
567:
533:
401:
Stefan Banach was born on 30 March 1892 at St. Lazarus General Hospital in
353:
346:
107:
85:
1717:"Stefan Banach (March 30, 1892 – August 8, 1945) – Mathematics in Europe"
1007:, which proved instrumental in the development of his scientific career.
989:
819:
naming of these spaces after him. The theory of what came to be known as
777:
550:
498:
191:
963:
955:
873:
1910:. Translated by Wojbor Andrzej Woyczyński and Ann Kostant. Birkhäuser.
1878:
974:
938:
for outstanding achievements in mathematical sciences. Since 2009, the
586:) also established a mathematical society, which eventually became the
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614:
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1038:
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537:
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293:
53:
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440:
959:
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at that time, including those of the famous Polish mathematicians
338:
comprising some of the most renowned Polish mathematicians of the
1762:
The Oxford Handbook of Generality in Mathematics and the Sciences
429:
421:
349:
1986:
1863:. Gdańsk University Press and Adam Mickiewicz University Press.
1791:. Institute of Mathematics, Polish Academy of Sciences: 57–108.
753:
685:
479:
326:, subsequently becoming a professor in 1922 and a member of the
1926:
1235:
947:
816:
738:
541:
474:
417:
410:
297:
1945:
Siegmund-Schultze, Reinhard (2003). Jahnke, Hans Niels (ed.).
1781:"Alfred Rosenblatt (1880–1947). Polish–Peruvian mathematician"
1669:"Stefan Banach: Google Doodle celebrates Polish mathematician"
1010:
In 2021, one of the episodes of Polish documentary TV series
765:
506:
1723:. Translated by Kramer, David. European Mathematical Society
1647:""Geniusze i marzyciele" – nowy serial dokumentalny w TVP1"
1015:
951:
827:(published in 1916) and contemporaneous contributions from
823:
had antecedents in the work of the Hungarian mathematician
680:
483:
77:
932:
Institute of Mathematics of the Polish Academy of Sciences
308:. After completing his secondary education, he befriended
768:, Banach began preparing to leave the city and settle in
1018:
and TVP Dokument channels was devoted to Stefan Banach.
478:(high school degree) at age 18 in 1910, Banach moved to
1760:
Chemla, Karine; Chorla, Renaud; Rabouin, David (2016).
877:
Decomposition of a ball into two identical balls – the
2189:
Members of the National Academy of Sciences of Ukraine
1860:
Stefan Banach - Remarkable life, Brilliant mathematics
1223:
1907:
Through a Reporter's Eyes: The Life of Stefan Banach
1885:
Remarkable Mathematicians: From Euler to von Neumann
1856:
1778:
1388:
1376:
1340:
1316:
1252:
1250:
995:
In 2016, a commemorative bench featuring Banach and
772:, Poland, where he had been promised a chair at the
1759:
1545:"PIERWSZY LAUREAT "THE INTERNATIONAL BANACH PRIZE""
1157:
1139:
316:in 1919 and later published the scientific journal
2034:
1882:
1241:
605:, meeting place of many famous Lwów mathematicians
521:, but little is known of that period of his life.
1944:
1247:
1201:
1051:, in his autobiography, quotes Banach as saying:
2149:People from the Kingdom of Galicia and Lodomeria
2125:
862:). The theorem did not require linearity of the
1831:Newsletter of the European Mathematical Society
451:In 1902, Banach, aged 10, enrolled in Kraków's
322:. In 1920, he received an assistantship at the
273:; 30 March 1892 – 31 August 1945) was a Polish
1066:"Banach was my greatest scientific discovery."
870:(in particular to any complete metric space).
1857:Jakimowicz, E.; Miranowicz, A., eds. (2007).
1779:Ciesielska, Danuta; Maligranda, Lech (2019).
1532:Institute of Mathematics: Stefan Banach Medal
1431:
330:in 1924. Banach was also a co-founder of the
1425:
1322:
1298:
1274:
1197:
1195:
1193:
1191:
854:) and other mathematicians (in particular
713:for almost two years. Banach, from 1939 a
2184:Members of the Polish Academy of Learning
1796:
1500:
1498:
1481:(in French; Theory of Linear Operations).
1415:
1413:
1411:
1409:
1394:
1358:
1346:
1262:
1163:
1102:Timeline of Polish science and technology
807:. In this work Banach called such spaces
803:and laid the foundations for the area of
572:On the Mean Convergence of Fourier Series
524:
2022:
1965:
1519:
1484:
1286:
1229:
1097:List of things named after Stefan Banach
1032:
872:
846:, based on earlier methods developed by
670:
661:Polish Academy of Sciences and Fine Arts
597:
528:
486:) with the intention of studying at the
1984:
1924:
1715:Strick, Heinz Klaus (3 November 2016).
1569:
1490:
1471:
1213:MacTutor History of Mathematics Archive
1188:
619:King John II Casimir University of Lwów
461:). While the school specialized in the
2179:Members of the Lwów Scientific Society
2126:
2056:
2001:
1903:
1837:
1714:
1515:
1513:
1495:
1458:
1419:
1406:
1400:
1364:
1352:
1328:
1304:
1292:
1280:
1268:
1145:
1129:"Stefan Banach - Polish Mathematician"
788:) was attended by hundreds of people.
1877:
1824:"Facts and Myths about Stefan Banach"
1572:Genialni. Lwowska Szkoła Matematyczna
1504:
709:, Lwów came under the control of the
424:region. Greczek was a soldier in the
2005:The Best Writing on Mathematics 2019
1821:
1689:
1370:
1334:
1310:
1256:
1123:
1121:
536:and Stefan Banach Memorial Bench in
285:. His major work was the 1932 book,
2035:Waksmundzka-Hajnos, Monika (2006).
1510:
554:park, Banach encountered Professor
13:
2049:
14:
2215:
2199:Deaths from lung cancer in Poland
2103:
1951:. American Mathematical Society.
1842:. American Mathematical Society.
1158:Chemla, Chorla & Rabouin 2016
1118:
1082:International Stefan Banach Prize
1014:(Geniuses and Dreamers) aired on
940:International Stefan Banach Prize
436:and worked as a domestic helper.
2063:Théorie des Opérations Linéaires
2037:"Wspomnienie o Stefanie Greczku"
1479:Théorie des opérations linéaires
1389:Ciesielska & Maligranda 2019
1377:Jakimowicz & Miranowicz 2007
1341:Jakimowicz & Miranowicz 2007
1317:Jakimowicz & Miranowicz 2007
813:Théorie des opérations linéaires
791:
352:that bear Banach's name include
287:Théorie des opérations linéaires
281:, and an original member of the
260:
31:
16:Polish mathematician (1892–1945)
2028:Poland in the Twentieth Century
2008:. Princeton: University Press.
1985:Urbanek, Mariusz (April 2002).
1708:
1683:
1661:
1639:
1613:
1588:
1563:
1537:
1525:
1444:
1047:, another mathematician of the
988:coin, silver 10-zloty coin and
666:
312:, with whom he established the
1968:Elementary Functional Analysis
1889:. Cambridge University Press.
1596:"Narodowy Bank Polski. Monety"
977:in 1997, was named after him.
913:
866:, and applied to any complete
719:Academy of Sciences of Ukraine
593:
1:
2119:Mathematics Genealogy Project
2110:Page devoted to Stefan Banach
1741:: CS1 maint: date and year (
1692:Adventures of a Mathematician
1574:. Warsaw: Wydawnictwo Iskry.
1107:
1092:List of Polish mathematicians
764:from annexed formerly Polish
465:, Banach and his best friend
396:
2194:Burials at Lychakiv Cemetery
1764:. Oxford: University Press.
1171:"Home Page of Stefan Banach"
1112:
844:Banach's fixed point theorem
611:Poland regained independence
164:Surjection of Fréchet spaces
98:Technical University of Lwów
7:
2068:Theory of Linear Operations
1838:Jahnke, Hans Niels (2003).
1690:Ulam, Stanislaw M. (1976).
1623:(in Polish). Archived from
1547:(in Polish). Archived from
1070:
928:Polish Mathematical Society
924:Nagroda im. Stefana Banacha
588:Polish Mathematical Society
314:Polish Mathematical Society
234:Other notable students
10:
2220:
2164:Lwów School of Mathematics
1966:MacCluer, Barbara (2008).
1785:Banach Center Publications
1752:
1534:Polish Academy of Sciences
1049:Lwów School of Mathematics
628:Polish Academy of Learning
544:(sculpted by Stefan Dousa)
386:Banach fixed-point theorem
332:Lwów School of Mathematics
328:Polish Academy of Learning
283:Lwów School of Mathematics
175:Polish Academy of Learning
128:Banach fixed-point theorem
1694:. Scribner. p. 203.
1570:Urbanek, Mariusz (2014).
1466:Teoria operacji liniowych
1160:, pp. 224, 225, 237.
1028:
999:was unveiled in Kraków's
926:) was established by the
758:Lvov–Sandomierz Offensive
721:, and on good terms with
247:
233:
223:
207:
197:
187:
180:
169:
103:
93:
66:
39:
30:
23:
2043:(11). Gdańsk University.
1925:Kosiedowski, Stanisław.
1436:(in French and Polish).
1218:University of St Andrews
969:In 2001, a minor planet
898:Banach–Steinhaus theorem
811:, but in his 1932 book,
743:Nazi concentration camps
582:, Alfred Rosenblatt and
374:Banach–Steinhaus theorem
132:Banach–Steinhaus theorem
2174:Lviv Polytechnic alumni
2002:Pitici, Mircea (2019).
1434:Fundamenta Mathematicae
1242:Waksmundzka-Hajnos 2006
982:National Bank of Poland
852:Banach–Schauder theorem
774:Jagiellonian University
511:Jagiellonian University
492:Jagiellonian University
407:Austro-Hungarian Empire
391:
140:Banach–Schauder theorem
2159:Polish Roman Catholics
2144:Scientists from Kraków
1904:Kałuża, Roman (1996).
1068:
1057:
1041:
934:established a special
903:Banach–Alaoglu theorem
881:
694:
606:
576:Władysław Ślebodziński
545:
525:Discovery by Steinhaus
420:, both natives of the
382:Banach–Alaoglu theorem
148:Banach–Alaoglu theorem
1948:A History of Analysis
1840:A History of Analysis
1721:Mathematics in Europe
1064:
1053:
1036:
1012:Geniusze i marzyciele
893:Banach–Tarski paradox
879:Banach–Tarski paradox
876:
860:Poincaré and Birkhoff
674:
657:correspondence member
601:
548:In 1916, in Kraków's
532:
430:baptismal certificate
426:Austro-Hungarian Army
366:Banach–Tarski paradox
302:mathematical problems
124:Banach–Tarski paradox
1987:"Geniusz: gen i już"
1822:Duda, Roman (2009).
1204:Robertson, Edmund F.
1077:Closed range theorem
908:Banach–Stone theorem
848:Charles Émile Picard
786:Cmentarz Łyczakowski
727:Operation Barbarossa
715:corresponding member
564:Lebesgue integration
472:After obtaining his
345:Some of the notable
218:Kazimierz Twardowski
152:Banach–Stone theorem
136:Banach–Mazur theorem
2204:Functional analysts
1454:. 16 November 2022.
1202:O'Connor, John J.;
936:Stefan Banach Medal
920:Stefan Banach Prize
886:Hahn–Banach theorem
805:functional analysis
801:normed vector space
766:eastern territories
560:"Lebesgue integral"
455:(also known as the
405:, then part of the
370:Hahn–Banach theorem
279:functional analysis
144:Hahn–Banach theorem
112:Functional analysis
2169:Operator theorists
2089:on 11 January 2014
1627:on 19 October 2016
1391:, pp. 57–108.
1175:kielich.amu.edu.pl
1042:
882:
699:invasion of Poland
695:
644:Studia Mathematica
632:University of Lwów
607:
584:Włodzimierz Stożek
546:
519:Kazimierz Żorawski
432:, she was born in
319:Studia Mathematica
202:University of Lwów
1870:978-83-7326-451-9
1581:978-83-244-0381-3
1135:. 27 August 2023.
1037:Banach monument,
782:Lychakiv Cemetery
748:After the Soviet
677:Lychakiv Cemetery
515:Stanisław Zaremba
378:Banach–Mazur game
336:school of thought
251:
250:
224:Doctoral students
209:Doctoral advisors
182:Scientific career
2211:
2098:
2096:
2094:
2088:
2082:. Archived from
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2031:
2019:
1998:
1981:
1962:
1941:
1939:
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1185:
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1181:
1167:
1161:
1155:
1149:
1143:
1137:
1136:
1125:
1062:said of Banach:
973:, discovered by
809:"class E-spaces"
675:Banach's grave,
488:Lwów Polytechnic
324:Lwów Polytechnic
272:
271:
270:
263:
259:
73:
49:
47:
35:
21:
20:
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2208:
2124:
2123:
2106:
2101:
2092:
2090:
2086:
2071:
2052:
2050:Further reading
2047:
2024:Stachura, Peter
2016:
1978:
1959:
1935:
1933:
1927:"Stefan Banach"
1918:
1897:
1871:
1850:
1826:
1798:10.4064/bc119-4
1772:
1755:
1750:
1734:
1733:
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1713:
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1702:
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1551:on 17 June 2015
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1477:Stefan Banach:
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1208:"Stefan Banach"
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992:2-zloty coin).
930:. In 1992, the
916:
794:
762:deporting Poles
669:
624:Antoni Łomnicki
596:
527:
458:Goetz Gymnasium
399:
394:
362:Banach measures
358:Banach algebras
340:interwar period
296:to a family of
266:
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257:
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228:Stanisław Mazur
216:
162:
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156:Banach manifold
154:
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94:Alma mater
89:
88:(today Ukraine)
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71:
62:
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58:Austria-Hungary
51:
45:
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26:
17:
12:
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2105:
2104:External links
2102:
2100:
2099:
2058:Banach, Stefan
2053:
2051:
2048:
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2032:
2020:
2015:978-0691198354
2014:
1999:
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1977:978-0387855288
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1833:(71). EMS: 29.
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1333:
1331:, pp. 3–4
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1273:
1271:, pp. 2–4
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1133:britannica.com
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1060:Hugo Steinhaus
1045:Stanislaw Ulam
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1005:Hugo Steinhaus
915:
912:
911:
910:
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833:Norbert Wiener
793:
790:
668:
665:
595:
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556:Hugo Steinhaus
526:
523:
482:(today called
467:Witold Wiłkosz
414:Roman Catholic
398:
395:
393:
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310:Hugo Steinhaus
304:during school
249:
248:
245:
244:
242:Stanislaw Ulam
238:Józef Schreier
235:
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120:Banach measure
116:Banach algebra
105:
104:Known for
101:
100:
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91:
90:
76:
74:(aged 53)
70:31 August 1945
68:
64:
63:
61:(today Poland)
52:
41:
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1771:9780198777267
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1701:9780684143910
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1528:
1521:
1520:MacCluer 2008
1516:
1514:
1507:, p. 384
1506:
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1258:
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1243:
1238:
1232:, p. 51.
1231:
1230:Stachura 1999
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1148:, p. 23.
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1103:
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1087:List of Poles
1085:
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1067:
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1024:
1023:Google Doodle
1019:
1017:
1013:
1008:
1006:
1002:
998:
993:
991:
987:
983:
980:In 2012, the
978:
976:
972:
967:
965:
961:
957:
953:
949:
944:
941:
937:
933:
929:
925:
921:
918:In 1946, the
909:
906:
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896:
894:
891:
890:
889:
887:
880:
875:
871:
869:
865:
861:
857:
853:
849:
845:
840:
838:
837:Banach spaces
834:
830:
826:
825:Frigyes Riesz
822:
821:Banach spaces
818:
814:
810:
806:
802:
799:
792:Contributions
789:
787:
783:
779:
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771:
767:
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736:
733:at Professor
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688:
687:
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646:
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639:Scottish Café
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633:
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603:Scottish Café
600:
591:
589:
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581:
580:Leon Chwistek
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363:
359:
355:
354:Banach spaces
351:
348:
343:
342:(1918–1939).
341:
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321:
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303:
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276:
275:mathematician
269:
262:
255:
254:Stefan Banach
246:
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206:
203:
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172:
168:
165:
161:
160:Banach bundle
157:
153:
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137:
133:
129:
125:
121:
117:
113:
109:
106:
102:
99:
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92:
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83:
82:Ukrainian SSR
79:
69:
65:
59:
55:
50:30 March 1892
42:
38:
34:
29:
25:Stefan Banach
22:
19:
2091:. Retrieved
2084:the original
2067:
2062:
2057:
2040:
2027:
2004:
1994:
1990:
1970:. Springer.
1967:
1947:
1934:. Retrieved
1930:
1906:
1884:
1859:
1839:
1830:
1788:
1784:
1761:
1725:. Retrieved
1720:
1710:
1691:
1685:
1673:. Retrieved
1663:
1651:. Retrieved
1641:
1629:. Retrieved
1625:the original
1615:
1603:. Retrieved
1590:
1571:
1565:
1553:. Retrieved
1549:the original
1539:
1527:
1491:Urbanek 2002
1486:
1478:
1473:
1465:
1460:
1446:
1437:
1433:
1427:
1403:, p. 23
1396:
1384:
1372:
1367:, p. 16
1360:
1355:, p. 13
1348:
1336:
1324:
1312:
1300:
1288:
1276:
1264:
1237:
1225:
1211:
1178:. Retrieved
1174:
1165:
1153:
1141:
1132:
1065:
1058:
1054:
1043:
1020:
1011:
1009:
997:Otto Nikodym
994:
979:
971:16856 Banach
968:
945:
923:
917:
883:
868:Cauchy space
841:
836:
812:
808:
795:
785:
747:
735:Rudolf Weigl
711:Soviet Union
707:Soviet Union
703:Nazi Germany
696:
684:
667:World War II
653:metric space
642:
636:
608:
571:
568:Otto Nikodym
559:
549:
547:
534:Otto Nikodym
503:Russian Army
496:
473:
471:
456:
453:IV Gymnasium
452:
450:
438:
400:
347:mathematical
344:
317:
291:
286:
253:
252:
198:Institutions
181:
173:Membership:
108:Banach space
86:Soviet Union
72:(1945-08-31)
18:
2139:1945 deaths
2134:1892 births
2030:. Springer.
1879:James, Ioan
1649:(in Polish)
1601:(in Polish)
1522:, p. 6
1420:Jahnke 2003
1401:Kałuża 1996
1365:Kałuża 1996
1353:Kałuża 1996
1329:Kałuża 1996
1305:Kałuża 1996
1295:, p. 3
1293:Kałuża 1996
1281:Kałuża 1996
1269:Kałuża 1996
1146:Pitici 2019
1001:Planty Park
990:Nordic Gold
914:Recognition
778:lung cancer
752:recaptured
731:lice feeder
663:in Kraków.
594:Interbellum
499:World War I
443:; he was a
192:Mathematics
2128:Categories
2080:0005.20901
1896:0521520940
1849:0821826239
1727:19 January
1505:James 2003
1108:References
975:Paul Comba
842:Likewise,
697:After the
463:humanities
397:Early life
384:, and the
46:1892-03-30
1815:213021027
1807:0137-6934
1675:11 August
1653:11 August
1631:11 August
1605:11 August
1555:11 August
1257:Duda 2009
1180:19 August
1113:Citations
1021:In 2022,
922:(Polish:
829:Hans Hahn
817:eponymous
615:doctorate
409:, into a
2060:(1932).
2026:(1999).
1991:Polityka
1931:Mój Lwów
1881:(2003).
1737:cite web
1071:See also
964:Jarosław
956:Świdnica
798:complete
750:Red Army
705:and the
350:concepts
292:Born in
2117:at the
2093:11 July
1997:(2348).
1753:Sources
856:Brouwer
756:in the
717:of the
659:of the
445:private
434:Borówna
422:Podhale
258:Polish:
2078:
2070:]
2012:
1974:
1955:
1936:20 May
1914:
1893:
1867:
1846:
1813:
1805:
1768:
1698:
1578:
1379:, p. 6
1319:, p. 4
1039:Kraków
1029:Quotes
948:Warsaw
770:Kraków
739:Typhus
723:Soviet
691:Polish
649:linear
551:Planty
542:Poland
538:Kraków
475:matura
418:Banach
403:Kraków
380:, the
376:, the
372:, the
368:, the
364:, the
306:recess
294:Kraków
188:Fields
170:Awards
54:Kraków
2087:(PDF)
2072:(PDF)
2066:[
2041:Focus
1827:(PDF)
1811:S2CID
1599:(PDF)
1343:, p.5
986:zloty
960:Toruń
864:space
689:, in
507:tutor
497:When
441:marry
411:Góral
298:Goral
264:
2095:2020
2010:ISBN
1972:ISBN
1953:ISBN
1938:2008
1912:ISBN
1891:ISBN
1865:ISBN
1844:ISBN
1803:ISSN
1766:ISBN
1743:link
1729:2024
1696:ISBN
1677:2022
1655:2022
1633:2022
1607:2022
1576:ISBN
1557:2022
1182:2017
1016:TVP1
962:and
952:Lviv
884:The
858:and
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686:Lwów
681:Lviv
517:and
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480:Lwów
392:Life
334:, a
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