457:. The older generation of his students includes L. A. Tumarkin, V. V. Nemytsky, A. N. Cherkasov, N. B. Vedenisov, G. S. Chogoshvili. The group of "Forties" includes Yu. M. Smirnov, K. A. Sitnikov, O. V. Lokutsievsky, E. F. Mishchenko, M. R. Shura-Bura. The generation of the fifties includes A.V. Arkhangelsky, B. A. Pasynkov, V. I. Ponomarev, as well as E. G. Sklyarenko and A. A. Maltsev, who were in graduate school under Yu.M. Smirnov and K. A. Sitnikov, respectively. The group of the youngest students is formed by V. V. Fedorchuk, V. I. Zaitsev and E. V. Shchepin.
314:, about whom he said: "In 1979 this friendship celebrated its fiftieth anniversary and over the whole of this half century there was not only never any breach in it, there was also never any quarrel, in all this time there was never any misunderstanding between us on any question, no matter how important for our lives and our philosophy; even when our opinions on one of these questions differed, we showed complete understanding and sympathy for the views of each other." Researchers have since conjectured that the two men were in a secret gay relationship.
53:
436:
Despite the fact that P. S. Alexandrov was a student of N. N. Luzin and one of the members of
Lusitania, during the persecution of Luzin (the Luzin Affair), Alexandrov was one of the most active persecutors of the scientist. Relations between Luzin and Alexandrov remained very strained until the end
844:
Kolmogorov alone among the top Soviet mathematicians avoided being drafted into the postwar military effort. His students always wondered why-and the only likely explanation seems to be
Kolmogorov's homosexuality. His lifelong partner, with whom he shared a home starting in 1929, was the topologist
358:
In 1924, Alexandrov proved that in every open cover of a separable metric space, a locally finite open cover can be inscribed (this very concept, one of the key concepts in general topology, was first introduced by
Alexandrov. In fact, this proved the paracompact nature of separable metric spaces
289:
is true. This still unsolved problem was too much for
Alexandrov and he had a creative crisis at the end of 1917. The failure was a heavy blow for Alexandrov: "It became clear to me that the work on the continuum problem ended in a serious disaster. I also felt that I could no longer move on to
370:
He significantly advanced the theory of dimension (in particular, he became the founder of the homological theory of dimension — its basic concepts were defined by
Alexandrov in 1932. He developed methods of combinatorial research of general topological spaces, proved a number of basic laws of
378:
were the founders of the Moscow topological school, which received international recognition. A number of concepts and theorems of topology bear
Alexandrov's name: the Alexandrov compactification, the Alexandrov-Hausdorff theorem on the cardinality of a-sets, the Alexandrov topology, and the
332:(Alexandrov himself called it "Bicompactness", and applied the term compact to only countably compact spaces, as was customary before him). Together with P. S. Urysohn, Alexandrov showed the full meaning of this concept; in particular, he proved the first general
293:
Alexandrov went to
Chernihiv, where he participated in the organization of the drama theater. "I met L. V. Sobinov there, who was at that time the head of the Department of Arts of the Ukrainian People's Commissariat of Education."
1088:
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1219:
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Alexandrov's main works are on topology, set theory, theory of functions of a real variable, geometry, calculus of variations, mathematical logic, and foundations of mathematics.
1224:
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1244:
1289:
1229:
343:, and he managed to combine this branch of topology with general topology and significantly advance the resulting theory, which became the basis for modern
1239:
1249:
783:
826:
The police soon learned of
Kolmogorov and Alexandrov's homosexual bond, and they used that knowledge to obtain the behavior that they wished.
646:
Pasynkov B. A. Introduction to the Theory of
Dimension. Introduction to the Theory of Topological Spaces and the General Theory of Dimensions
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17:
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1234:
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In 1936, Alexandrov was an active participant in the political offensive against his former mentor Luzin that is known as the
971:
819:
725:
300:
In 1921, he married
Ekaterina Romanovna Eiges (1890-1958) who was a poet and memoirist, library worker and mathematician.
1254:
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in 1923 and 1924. After getting his Ph.D. in 1927, he continued to work at Moscow State University and also joined the
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535:
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It was generally known that they had a homosexual relationship, although they never acknowledged their liaison
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mathematics and, so to speak, to the next tasks, and that some decisive turning point must come in my life."
187:
171:
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1112:
988:
720:] (in Russian) (3rd, expanded ed.). Moscow: Moscow University Publishing House. pp. 127–133.
492:
231:
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topological duality. In 1927, he generalized Alexander's theorem to the case of an arbitrary closed set.
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and the famous compactification theorem of any locally compact Hausdorff space by adding a single point.
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247:
128:
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This article is about the Moscow-based mathematician. For the Leningrad-based mathematician, see
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347:. It was he who introduced one of the basic concepts of algebraic topology — the concept of an
340:
1002:(3 (159)) (Advances in Mathematical Sciences ed.). Russian Academy of Sciences: 161–164.
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858:
792:
383:
889:
Pricing the Future: Finance, Physics, and the 300-year Journey to the Black-Scholes Equation
1279:
1204:
1199:
1003:
355:, which led him (independently of E. Cech) to the discovery of Alexandrov-Cech Cohomology.
286:
601:
Theory of Dimensionality and Related Issues. Articles of a General Bature (Selected Works)
317:
He was buried at the Kavezinsky cemetery of the Pushkinsky district of the Moscow region.
8:
1184:
1141:
364:
352:
333:
235:
1007:
712:
Sadovnichy, Viktor Antonovich (2019). "Aleksandr Nikolayevich Nesmeyanov (1899—1980)".
222:
mathematician. He wrote roughly three hundred papers, making important contributions to
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524:
344:
81:
740:
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Theory of Functions of Real Variable and Theory of Topological Spaces (Selected Works)
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967:
893:
864:
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569:
550:
531:
311:
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360:
1011:
958:
Sadovnichy, Viktor Antonovich (2015). "Pavel Sergeyevich Alexandrov (1896—1982)".
471:
207:
152:
915:
935:] (in Ukrainian). Kyiv: Наукова думка (Scientific thought). pp. 127–128.
860:
Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity
808:
Naming infinity: a true story of religious mysticism and mathematical creativity
437:
of Luzin's life, and Alexandrov became an academician only after Luzin's death.
619:
Introduction to Homological Dimension Theory and General Combinatorial Topology
476:
348:
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During this period, Alexandrov visited Denikin prison and was ill with typhus.
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Lorentz G.G., Mathematics and Politics in the Soviet Union from 1928 to 1953
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966:] (in Russian). Moscow: Moscow University Publishing House. p. 96.
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118:
107:
145:
840:
Perfect Rigour: A Genius and the Mathematical Breakthrough of a Lifetime
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His books played an important role in the development of science and
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Band 1 — Berlin) became the classic course of topology of its time.
303:
In 1955, he signed the "Letter of Three Hundred" with criticism of
227:
77:
753:"To the 50th anniversary of the "Letters of the Three Hundred""
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Member of the United States National Academy of Sciences (1947)
367:
showed that the requirement of separability can be abandoned).
103:
34:. For the lawyer and state official of the Russian Empire, see
1057:
791:(2). Centrum Wiskunde & Informatica: 3–18. Archived from
445:
Among the students of P. S. Alexandrov, the most famous are
1285:
Members of the Göttingen Academy of Sciences and Humanities
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1033:
1069:
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359:(although the term "paracompact space" was introduced by
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Academicians of the USSR Academy of Pedagogical Sciences
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1030:
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Introduction to the General Theory of Sets and Functions
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Foreign associates of the National Academy of Sciences
1185:
Kutateladze S.S., The Tragedy of Mathematics in Russia
933:
Mathematicians. Mechanics. Biographical reference book
989:"Eduard Cech (to the tenth anniversary of his death)"
1270:
Recipients of the Order of the Red Banner of Labour
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Members of the German Academy of Sciences at Berlin
479:, six times (1946, 1953, 1961, 1966, 1969 and 1975)
523:
1139:
691:Topological Duality Theorems. Part 1. Closed Sets
682:Uryson P. S. Memoir on Compact Topological Spaces
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673:Course of Analytical Geometry and Linear Algebra
285:Luzin challenged Alexandrov to determine if the
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929:Математики. Механики. Биографический справочник
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637:Introduction to set Theory and General Topology
610:The General Theory of homology (Selected Works)
806:Graham, Loren R.; Kantor, Jean-Michel (2009).
1290:Members of the American Philosophical Society
351:. Alexandrov also introduced the notion of a
1230:Full Members of the USSR Academy of Sciences
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805:
404:Introduction to Homological Dimension Theory
1240:Members of the Austrian Academy of Sciences
857:Graham, Loren; Kantor, Jean-Michel (2009),
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670:
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379:Alexandrov — Cech homology and cohomology.
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666:. Moscow: Academy of Pedagogical Sciences.
417:in German (Alexandroff P., Hopf H. (1935)
339:From 1923 P. S. Alexandrov began to study
1250:Academic staff of Moscow State University
863:, Harvard University Press, p. 185,
927:Bogolyubov, Alexey Nikolaevich (1983).
1175:MacTutor History of Mathematics archive
1151:MacTutor History of Mathematics Archive
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566:An introduction to the theory of groups
218:(7 May 1896 – 16 November 1982), was a
14:
1192:
882:
837:
770:
320:
310:Alexandrov made lifelong friends with
964:About the people of Moscow University
718:About the people of Moscow University
460:
916:Pushkinsky district of Moscow region
628:Introduction to the Theory of Groups
568:. Mineola, N.Y: Dover Publications.
549:. Mineola, N.Y: Dover Publications.
1210:20th-century Russian mathematicians
583:
424:
402:(together with B. A. Pasynkov) and
24:
25:
1306:
1295:Recipients of the Cothenius Medal
1235:Imperial Moscow University alumni
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488:Order of the Red Banner of Labour
328:He introduced the new concept of
1265:Recipients of the Order of Lenin
960:О людях Московского университета
714:О людях Московского университета
280:
268:Steklov Institute of Mathematics
51:
32:Aleksandr Danilovich Aleksandrov
27:Soviet mathematician (1896–1982)
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1016:10.1070/RM1971v026n03ABEH003833
980:
951:
920:
779:"Andrei Nikolaevich Kolmogorov"
526:Elementary concepts of topology
483:Order of the October Revolution
396:Lectures on Analytical Geometry
1260:Recipients of the Stalin Prize
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876:
850:
842:. Icon Books Ltd. p. 17.
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734:
705:
664:What is Non-euclidean Geometry
499:American Philosophical Society
212:Па́вел Серге́евич Алекса́ндров
36:Pavel Alexandrovich Alexandrov
13:
1:
1166:Mathematics Genealogy Project
996:Russian Mathematical Surveys
892:, Basic Books, p. 152,
493:Order of the Badge of Honour
273:He was made a member of the
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232:Alexandroff compactification
204:Pavel Sergeyevich Alexandrov
64:Pavel Sergeyevich Alexandrov
18:Pavel Sergeevich Aleksandrov
7:
689:Aleksandrov, P. S. (1955).
680:Aleksandrov, P. S. (1971).
671:Aleksandrov, P. S. (1979).
662:Aleksandrov, P. S. (1950).
653:Aleksandrov, P. S. (1947).
644:Aleksandrov, P. S. (1973).
635:Aleksandrov, P. S. (1977).
626:Aleksandrov, P. S. (1980).
617:Aleksandrov, P. S. (1975).
608:Aleksandrov, P. S. (1979).
599:Aleksandrov, P. S. (1978).
590:Aleksandrov, P. S. (1978).
564:Aleksandrov, P. S. (2012).
545:Aleksandrov, P. S. (1998).
522:Aleksandrov, P. S. (1961).
440:
275:Russian Academy of Sciences
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1255:Heroes of Socialist Labour
250:where he was a student of
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518:Topologie Bd.1 — B:, 1935
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1156:University of St Andrews
987:Chernavsky A.V. (1971).
959:
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812:Harvard University Press
777:Vitányi, P.M.B. (1988).
713:
698:
508:
467:Hero of Socialist Labour
413:, written together with
264:University of Göttingen
248:Moscow State University
214:), sometimes romanized
129:Moscow State University
838:Gessen, Masha (2011).
741:Memoirs of E. R. Eiges
655:Combinatorial Topology
547:Combinatorial topology
392:Combinatorial Topology
341:combinatorial topology
1275:Soviet mathematicians
1171:The 1936 Luzin affair
1113:"Paul S. Alexandroff"
384:mathematics education
363:in 1944, and in 1948
238:are named after him.
1142:Robertson, Edmund F.
1093:search.amphilsoc.org
1089:"APS Member History"
657:. Moscow: Fizmatgiz.
287:continuum hypothesis
246:Alexandrov attended
1215:People from Noginsk
1140:O'Connor, John J.;
1066:, pp. 127–128.
1008:1971RuMaS..26..177C
530:. New York: Dover.
365:Arthur Harold Stone
353:nerve of a covering
334:metrization theorem
321:Scientific activity
236:Alexandrov topology
230:. In topology, the
1146:"Pavel Alexandrov"
693:. Moscow: AS USSR.
461:Honours and awards
345:algebraic topology
82:Moscow Governorate
1117:www.nasonline.org
973:978-5-19-011041-8
845:Pavel Alexandrov.
821:978-0-674-03293-4
766:(1): 12–33. 2005.
727:978-5-19-011397-6
312:Andrey Kolmogorov
262:, he visited the
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168:Doctoral students
136:Scientific career
16:(Redirected from
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621:. Moscow: Nauka.
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594:. Moscow: Nauka.
584:Books In Russian
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541:
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514:Alexandroff P.,
455:Aleksandr Kurosh
451:Andrey Tychonoff
425:The Luzin Affair
400:Dimension Theory
258:. Together with
216:Paul Alexandroff
213:
172:Aleksandr Kurosh
153:Doctoral advisor
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96:16 November 1982
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1052:Sadovnichy 2015
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998:(in Russian).
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1200:1896 births
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330:compactness
146:Mathematics
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1194:Categories
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