Karol Borsuk (May 8, 1905 – January 24, 1982) was a Polish mathematician.
His main interest was
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 ...
, while he obtained significant results also in
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defi ...
.
Borsuk introduced the theory of ''
absolute retracts'' (ARs) and ''
absolute neighborhood retract
In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace. The subspace is then called a retract of the original space. A deforma ...
s'' (ANRs), and the
cohomotopy groups, later called Borsuk–
Spanier cohomotopy groups. He also founded
shape theory. He has constructed various beautiful examples of
topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called poin ...
s, e.g. an acyclic, 3-dimensional
continuum which admits a fixed point free
homeomorphism
In the mathematical field of topology, a homeomorphism, topological isomorphism, or bicontinuous function is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isom ...
onto itself; also 2-dimensional, contractible polyhedra which have no free edge. His topological and geometric conjectures and themes stimulated research for more than half a century; in particular, his open problems stimulated the
infinite-dimensional topology
In mathematics, the dimension of a vector space ''V'' is the cardinality (i.e., the number of vectors) of a basis of ''V'' over its base field. p. 44, §2.36 It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to dist ...
.
Borsuk received his
master's degree
A master's degree (from Latin ) is an academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice. and
doctorate
A doctorate (from Latin ''docere'', "to teach"), doctor's degree (from Latin ''doctor'', "teacher"), or doctoral degree is an academic degree awarded by universities and some other educational institutions, derived from the ancient formalism ''l ...
from
Warsaw University
The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...
in 1927 and 1930, respectively; his
PhD PHD or PhD may refer to:
* Doctor of Philosophy (PhD), an academic qualification
Entertainment
* '' PhD: Phantasy Degree'', a Korean comic series
* '' Piled Higher and Deeper'', a web comic
* Ph.D. (band), a 1980s British group
** Ph.D. (Ph.D. al ...
thesis advisor was
Stefan Mazurkiewicz
Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning (''PAU''). ...
. He was a member of the
Polish Academy of Sciences
The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society o ...
from 1952. Borsuk's students included
Samuel Eilenberg
Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish-American mathematician who co-founded category theory (with Saunders Mac Lane) and homological algebra.
Early life and education
He was born in Warsaw, Kingdom of Poland to ...
, Włodzimierz Holsztyński,
Jan Jaworowski,
Krystyna Kuperberg
Krystyna M. Kuperberg (born ''Krystyna M. Trybulec''; 17 July 1944) is a Polish-American mathematician who currently works as a professor of mathematics at Auburn University, where she was formerly an Alumni Professor of Mathematics.[Włodzimierz Kuperberg
Włodzimierz Kuperberg (born January 19, 1941) is a professor of mathematics at Auburn University, with research interests in geometry and topology.
Biography
Although Kuperberg is Polish-American, he was born in what is now Belarus, where his ...]
, Hanna Patkowska, and
Andrzej Trybulec.
Works
* ''Geometria analityczna w n wymiarach'' (1950) (translated to English as ''Multidimensional Analytic Geometry'',
Polish Scientific Publishers
Wydawnictwo Naukowe PWN (''Polish Scientific Publishers PWN''; until 1991 ''Państwowe Wydawnictwo Naukowe'' - ''National Scientific Publishers PWN'', PWN) is a Polish book publisher, founded in 1951, when it split from the Wydawnictwa Szkolne i P ...
, 1969)
* ''Podstawy geometrii'' (1955)
* ''Foundations of Geometry'' (1960) with
Wanda Szmielew
Wanda Szmielew née Montlak (5 April 1918 – 27 August 1976) was a Polish mathematical logician who first proved the decidability of the first-order theory of abelian groups.
Life
Wanda Montlak was born on 5 April 1918 in Warsaw. She complet ...
, North Holland publisher
* ''Theory of Retracts'' (1967), PWN, Warszawa.
* ''Theory of Shape'' (1975)
* ''Collected papers'' vol. I, (1983), PWN, Warszawa.
See also
*
Bing–Borsuk conjecture In mathematics, the Bing–Borsuk conjecture states that every n-dimensional homogeneous absolute neighborhood retract space is a topological manifold. The conjecture has been proved for dimensions 1 and 2, and it is known that the 3-dimensional ve ...
*
Borsuk's conjecture
The Borsuk problem in geometry, for historical reasons incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk.
Problem
In 1932, Karol Borsuk showed that an ordinary 3-dimensional ball in Euclid ...
*
Borsuk–Ulam theorem
*
Zygmunt Janiszewski
Zygmunt Janiszewski (12 July 1888 – 3 January 1920) was a Polish mathematician.
Early life and education
He was born to mother Julia Szulc-Chojnicka and father, Czeslaw Janiszewski who was a graduate of the University of Warsaw and served as t ...
*
Stanislaw Ulam
Stanisław Marcin Ulam (; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in the Manhattan Project, originated the Teller–Ulam design of thermonuclear weapon ...
*
Scottish Café
The Scottish Café ( pl, Kawiarnia Szkocka) was a café in Lwów, Poland (now Lviv, Ukraine) where, in the 1930s and 1940s, mathematicians from the Lwów School of Mathematics collaboratively discussed research problems, particularly in fun ...
*
Animal Husbandry
Animal husbandry is the branch of agriculture concerned with animals that are raised for meat, fibre, milk, or other products. It includes day-to-day care, selective breeding, and the raising of livestock. Husbandry has a long history, starti ...
, an educational
dice game published by Borsuk at his own expense in 1943 during the
German occupation of Warsaw. The original game was lost during the Warsaw uprising in August 1944. Very few copies survived outside Warsaw and one was given back to the Borsuk family. The game is now published by Granna under the name of "Super Farmer".
References
External links
*
*
{{DEFAULTSORT:Borsuk, Karol
Warsaw School of Mathematics
Topologists
Members of the Polish Academy of Sciences
University of Warsaw alumni
University of Warsaw faculty
People from Warsaw Governorate
1905 births
1982 deaths