Pavel Samuilovich Urysohn () (February 3, 1898 – August 17, 1924) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nationa ...

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, structure, space, models, and change. History ...

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 coordin ...

, 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, \mathcal) is said to be metrizable if there is a metric d : X \times X \to , \infty) ...

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 continu ...

, both of which are fundamental results in

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

. His name is also commemorated in the terms Urysohn universal space,

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 speci ...

, Menger–Urysohn dimension and Urysohn integral equation. He and

Pavel Alexandrov Pavel Sergeyevich Alexandrov (russian: Па́вел Серге́евич Алекса́ндров), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote about three hundred papers, ma ...

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 by making precise the idea of a space having no "punctures" or "missing endpoints", i ...

in 1923.

Biography

Born in 1898 in

Odessa Odesa (also spelled Odessa) is the third most populous city and municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern shore of the Black Sea. The city is also the administrativ ...

, Urysohn studied at

Moscow University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

from 1915 to 1921. His advisor was

Nikolai Luzin Nikolai Nikolaevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlaɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 January 1950) was a Soviet/ R ...

. He then became an assistant professor there. He drowned in 1924 while swimming off the coast of

Brittany Brittany (; french: link=no, Bretagne ; br, Breizh, or ; Gallo: ''Bertaèyn'' ) is a peninsula, historical country and cultural area in the west of modern France, covering the western part of what was known as Armorica during the period ...

, France, near

Batz-sur-Mer Batz-sur-Mer (, literally ''Batz on Sea''; br, Bourc'h-Baz) is a commune in the Loire-Atlantique department in western France. The commune is situated on a former island that, until around the 9th century, was separate from the mainland at ...

, and is buried there. 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,

Lazar Lyusternik Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899, in Zduńska Wola, Congress Poland, Russian Empire – 23 July 1981, in Moscow, Soviet Union) was a Soviet mathematician. He is famous for his work in topolo ...

, and

Mark Krasnosel'skii Mark Aleksandrovich Krasnoselsky (russian: Ма́рк Алекса́ндрович Красносе́льский; 27 April 1920, Starokostiantyniv – 13 February 1997, Moscow) was a Soviet and Russian mathematician renowned for his work on ...

References

* Pavel Urysohn, ''Sur une classe d'equations integrales non lineaires'', Mat. Sb. 31 (1923) 256–255
MacTutor biography of Urysohn
* * L. Neiman,

' (''Joy of Discovery''), Det. Lit., Moscow, 1972 (in Russian). 20th-century Russian mathematicians Moscow State University alumni Moscow State University faculty Topologists Deaths by drowning 1898 births 1924 deaths Accidental deaths in France Scientists from Odesa {{Russia-mathematician-stub