Pavel Samuilovich Urysohn (in

Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

: ; 3 February, 1898 – 17 August, 1924) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who is best known for his contributions in

dimension theory In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...

, and for developing

Urysohn's metrization theorem In topology and related areas of mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space (X, \tau) is said to be metrizable if there is a metric d : X \times X \to , \infty) such ...

and

Urysohn's lemma In topology, Urysohn's lemma is a lemma that states that a topological space is normal if and only if any two disjoint closed subsets can be separated by a continuous function. Section 15. Urysohn's lemma is commonly used to construct contin ...

, both of which are fundamental results in

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

. He also constructed what is now called the

Urysohn universal space The Urysohn universal space is a certain metric space that contains all separable metric spaces in a particularly nice manner. This mathematics concept is due to Pavel Urysohn, who presented an explicit construction. Another construction has been ...

and his name is also commemorated in the terms

Fréchet–Urysohn space In the field of topology, a Fréchet–Urysohn space is a topological space X with the property that for every subset S \subseteq X the closure of S in X is identical to the ''sequential'' closure of S in X. Fréchet–Urysohn spaces are a spec ...

Menger–Urysohn dimension In the mathematical field of topology, the inductive dimension of a topological space ''X'' is either of two values, the small inductive dimension ind(''X'') or the large inductive dimension Ind(''X''). These are based on the observation that, in ' ...

and

Urysohn integral equation Pavel Samuilovich Urysohn (in Russian: ; 3 February, 1898 – 17 August, 1924) was a Soviet mathematician who is best known for his contributions in dimension theory, and for developing Urysohn's metrization theorem and Urysohn's lemma, both of w ...

. He and

Pavel Alexandrov Pavel Sergeyevich Alexandrov (), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote roughly three hundred papers, making important contributions to set theory and topology. In topol ...

formulated the modern definition of

compactness In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it ...

in 1923.

Biography

Pavel Urysohn was born in

Odesa Odesa, also spelled Odessa, is the third most populous List of cities in Ukraine, city and List of hromadas of Ukraine, municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern ...

in 1898. His mother died when he was little, and he entered the care of his father and sister. The family moved to

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

in 1912, where Urysohn completed his secondary education. While still at school, he worked at Shanyavsky University on an experimental project on X-ray radiation and was supervised by

Petr Lazarev Petr Petrovich Lazarev (; 14 April 1878 – 24 April 1942) was a biophysicist and a founder of the Soviet Institute of Physics and Biophysics (now Lebedev Physical Institute). He also founded the journal ''Uspekhi fizicheskikh nauk'' (later '' Ph ...

. At that time, Urysohn’s interests lay predominantly in physics. Urysohn enrolled at the Moscow State University in 1915 and earned his Bachelor of science in 1919. There he attended the lectures of

Nikolai Luzin Nikolai Nikolayevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlajɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 February 1950) was a Sov ...

and Dimitri Egorov, which made him turn his attention to mathematics. Between 1919 and 1921, Urysohn completed a doctorate on integral equations under the supervision of Luzin. He then became an assistant professor at

Moscow University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, and six branches. Al ...

, and Egorov prompted him to start working in topology. By 1922, Urysohn had given topological definitions to curve, surface, and dimension, and his work attracted the attention of many prominent European mathematicians. In the summers of 1923 and 1924, Urysohn and his friend and fellow mathematician,

Pavel Aleksandrov Pavel Sergeyevich Alexandrov (), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote roughly three hundred papers, making important contributions to set theory and topology. In topol ...

, traveled through France, Holland, and Germany, where they met

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

Felix Hausdorff Felix Hausdorff ( , ; November 8, 1868 – January 26, 1942) was a German mathematician, pseudonym Paul Mongré (''à mogré' (Fr.) = "according to my taste"), who is considered to be one of the founders of modern topology and who contributed sig ...

, and

L. E. J. Brouwer Luitzen Egbertus Jan "Bertus" Brouwer (27 February 1881 – 2 December 1966) was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis. Regarded as one of the greatest mathematicians of the ...

. The three European mathematicians were impressed by Urysohn’s work and expressed their hopes that he would visit them again in subsequent years. Urysohn and Aleksandrov were staying in a cottage in

Brittany Brittany ( ) is a peninsula, historical country and cultural area in the north-west of modern France, covering the western part of what was known as Armorica in Roman Gaul. It became an Kingdom of Brittany, independent kingdom and then a Duch ...

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

, when Urysohn drowned at the age of 26 while swimming off the coast nearby

Batz-sur-Mer Batz-sur-Mer (, literally ''Batz on Sea''; Gallo language, Gallo: ''Borg-de-Baz'', ) is a Communes of France, commune in the Loire-Atlantique Departments of France, department in western France. The commune is situated on a former island, which ...

. Urysohn's sister, Lina Neiman, wrote a memoir about his life and childhood. Not being a mathematician, she included in the book memorial articles about his mathematical works by

, Vadim Efremovich,

Andrei Kolmogorov Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet ...

Lazar Lyusternik Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899 – 22 July 1981) was a Soviet mathematician. He is famous for his work in topology and differential geometry, to which he applied the variational principle. U ...

, and

Mark Krasnosel'skii Mark Aleksandrovich Krasnoselsky (; 27 April 1920, Starokostiantyniv – 13 February 1997, Moscow) or Mark Alexsandrovich Krasnoselskii was a Soviet and Russian mathematician renowned for his work on nonlinear functional analysis and its appl ...

References

20th-century Russian mathematicians Moscow State University alumni Academic staff of Moscow State University Topologists 1898 births 1924 deaths Scientists from Odesa Russian scientists Deaths by drowning in France {{Russia-mathematician-stub