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{{Short description|Polish mathematician (1905–1982)}}
{{Infobox scientist
{{Infobox scientist
|name = Karol Borsuk
|name = Karol Borsuk
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|image_size =
|image_size =
|caption =
|caption =
|birth_date = {{birth date|1905|5|8}}
|birth_date = {{birth date|1905|5|8|df=y}}
|birth_place = [[Warsaw]], [[Vistula Land]], [[Russian Empire]]
|birth_place = [[Warsaw]], [[Vistula Land]], [[Russian Empire]]
|death_date = {{death date and age|1982|1|24|1905|5|8}}
|death_date = {{death date and age|1982|1|24|1905|5|8|df=y}}
|death_place = [[Warsaw]], [[People's Republic of Poland|Poland]]
|death_place = [[Warsaw]], [[People's Republic of Poland|Poland]]
|residence =
|residence =
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*[[Włodzimierz Kuperberg]]
*[[Włodzimierz Kuperberg]]
*[[Andrzej Trybulec]]
*[[Andrzej Trybulec]]
*[[Krzysztof Edward Haman]]
}}
}}
|known_for = [[Borsuk's conjecture]]<br>[[Borsuk–Ulam theorem]]
|known_for = [[Borsuk's conjecture]]<br>[[Borsuk–Ulam theorem]]<br>[[Bing–Borsuk conjecture]]
|author_abbrev_bot =
|author_abbrev_bot =
|author_abbrev_zoo =
|author_abbrev_zoo =
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}}
}}


'''Karol Borsuk''' (May 8, 1905 – January 24, 1982) was a [[Poland|Polish]] mathematician.
'''Karol Borsuk''' (8 May 1905 – 24 January 1982) was a Polish mathematician.
His main interest was [[topology]].
His main interest was [[topology]], while he obtained significant results also in [[functional analysis]].


Borsuk introduced the theory of ''[[absolute retract]]s'' (ARs) and ''[[absolute neighborhood retract]]s'' (ANRs), and the [[cohomotopy group]]s, later called Borsuk–[[Edwin Spanier|Spanier]] cohomotopy groups. He also founded [[Shape theory (mathematics)|shape theory]]. He has constructed various beautiful examples of [[topological space]]s, e.g. an acyclic, 3-dimensional [[continuum (topology)|continuum]] which admits a fixed point free [[homeomorphism]] 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.
Borsuk introduced the theory of ''[[absolute retract]]s'' (ARs) and ''[[absolute neighborhood retract]]s'' (ANRs), and the [[cohomotopy group]]s, later called Borsuk–[[Edwin Spanier|Spanier]] cohomotopy groups. He also founded [[Shape theory (mathematics)|shape theory]]. He has constructed various beautiful examples of [[topological space]]s, e.g. an acyclic, 3-dimensional [[continuum (topology)|continuum]] which admits a fixed point free [[homeomorphism]] 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]].


Borsuk received his [[master's degree]] and [[doctorate]] from [[Warsaw University]] in 1927 and 1930, respectively; his [[Ph.D.]] thesis advisor was [[Stefan Mazurkiewicz]]. He was a member of the [[Polish Academy of Sciences]] from 1952. Borsuk's students included [[Samuel Eilenberg]], Włodzimierz Holsztyński, [[Jan Jaworowski]], [[Krystyna Kuperberg]], [[Włodzimierz Kuperberg]], and [[Andrzej Trybulec]].
Borsuk received his [[master's degree]] and [[doctorate]] from [[Warsaw University]] in 1927 and 1930, respectively; his [[PhD]] thesis advisor was [[Stefan Mazurkiewicz]]. He was a member of the [[Polish Academy of Sciences]] from 1952. Borsuk's students include: [[Samuel Eilenberg]], [[Andrzej Kirkor]], [[Jan Jaworowski]], [[Andrzej Granas]], [[Antoni Kosiński]], [[Karol Sieklucki]], [[Włodzimierz Holsztyński]], [[Rafał Molski]], [[Hanna Patkowska]], [[Andrzej Jankowski]], [[Włodzimierz Kuperberg]], [[Stanisław Spież]], [[Krystyna Kuperberg]], [[Jerzy Dydak]], [[Andrzej Trybulec]], [[Marian Orłowski]], [[Alfred Surzycki]].<ref>{{MathGenealogy|12548}}</ref>


==Works==
==Works==
* ''Geometria analityczna w n wymiarach'' (1950) (translated to English as ''Multidimensional Analytic Geometry'', [[Polish Scientific Publishers]], 1969)
* ''Geometria analityczna w n wymiarach'' (1950) (translated to English as ''Multidimensional Analytic Geometry'', [[Polish Scientific Publishers]], 1969)
* ''Podstawy geometrii'' (1955)
* ''Podstawy geometrii'' (1955)
* ''Foundations of Geometry'' (1960) with [[Wanda Szmielew]], North Holland publisher<ref>{{cite journal|author=Freudenthal, H.|authorlink=Hans Freudenthal|title=Review: ''Foundations of geometry, Euclidean and Bolyai–Lobachevskian geometry, projective geometry''. By K. Borsuk and Wanda Szmielew. Revised English translation.|journal=Bull. Amer. Math. Soc.|year=1961|volume=67|issue=4|pages=342–344|url=http://www.ams.org/journals/bull/1961-67-04/S0002-9904-1961-10606-X/S0002-9904-1961-10606-X.pdf|doi=10.1090/s0002-9904-1961-10606-x}}</ref>
* ''Foundations of Geometry'' (1960) with [[Wanda Szmielew]], North Holland publisher<ref>{{cite journal|author=Freudenthal, H.|authorlink=Hans Freudenthal|title=Review: ''Foundations of geometry, Euclidean and Bolyai–Lobachevskian geometry, projective geometry''. By K. Borsuk and Wanda Szmielew. Revised English translation.|journal=Bull. Amer. Math. Soc.|year=1961|volume=67|issue=4|pages=342–344|url=https://www.ams.org/journals/bull/1961-67-04/S0002-9904-1961-10606-X/S0002-9904-1961-10606-X.pdf|doi=10.1090/s0002-9904-1961-10606-x|doi-access=free}}</ref>
* ''Theory of Retracts'' (1967), PWN, Warszawa.
* ''Theory of Retracts'' (1967), PWN, Warszawa.
* ''Theory of Shape'' (1975)
* ''Theory of Shape'' (1975)
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==See also==
==See also==
* [[Bing–Borsuk conjecture]]
* [[Borsuk's conjecture]]
* [[Borsuk–Ulam theorem]]
* [[Zygmunt Janiszewski]]
* [[Zygmunt Janiszewski]]
* [[Stanislaw Ulam]]
* [[Stanislaw Ulam]]
* [[Scottish Café]]
* [[Scottish Café]]
* [[Animal Husbandry (game)|Animal Husbandry]], an educational [[dice game]] published by Borsuk at his own expense in 1943 during the [[German occupation of Warsaw]].
* [[Animal Husbandry (game)|Animal Husbandry]], 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==
==References==
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{{DEFAULTSORT:Borsuk, Karol}}
{{DEFAULTSORT:Borsuk, Karol}}
[[Category:20th-century Polish mathematicians]]
[[Category:Warsaw School of Mathematics]]
[[Category:Topologists]]
[[Category:Topologists]]
[[Category:Members of the Polish Academy of Sciences]]
[[Category:Members of the Polish Academy of Sciences]]
[[Category:University of Warsaw alumni]]
[[Category:University of Warsaw alumni]]
[[Category:University of Warsaw faculty]]
[[Category:Academic staff of the University of Warsaw]]
[[Category:People from Warsaw Governorate]]
[[Category:People from Warsaw Governorate]]
[[Category:1905 births]]
[[Category:1905 births]]
[[Category:1982 deaths]]
[[Category:1982 deaths]]
[[Category:Prisoners of Dulag 121 Pruszków]]
[[Category:Recipients of the Medal of the 10th Anniversary of the People's Republic of Poland]]

Latest revision as of 19:53, 23 May 2024

Karol Borsuk
Born(1905-05-08)8 May 1905
Warsaw, Vistula Land, Russian Empire
Died24 January 1982(1982-01-24) (aged 76)
Warsaw, Poland
NationalityPolish
Alma materWarsaw University
Known forBorsuk's conjecture
Borsuk–Ulam theorem
Bing–Borsuk conjecture
Scientific career
FieldsMathematics
Doctoral advisorStefan Mazurkiewicz
Notable students

Karol Borsuk (8 May 1905 – 24 January 1982) was a Polish mathematician. His main interest was topology, while he obtained significant results also in functional analysis.

Borsuk introduced the theory of absolute retracts (ARs) and absolute neighborhood retracts (ANRs), and the cohomotopy groups, later called Borsuk–Spanier cohomotopy groups. He also founded shape theory. He has constructed various beautiful examples of topological spaces, e.g. an acyclic, 3-dimensional continuum which admits a fixed point free homeomorphism 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.

Borsuk received his master's degree and doctorate from Warsaw University in 1927 and 1930, respectively; his PhD thesis advisor was Stefan Mazurkiewicz. He was a member of the Polish Academy of Sciences from 1952. Borsuk's students include: Samuel Eilenberg, Andrzej Kirkor, Jan Jaworowski, Andrzej Granas, Antoni Kosiński, Karol Sieklucki, Włodzimierz Holsztyński, Rafał Molski, Hanna Patkowska, Andrzej Jankowski, Włodzimierz Kuperberg, Stanisław Spież, Krystyna Kuperberg, Jerzy Dydak, Andrzej Trybulec, Marian Orłowski, Alfred Surzycki.[1]

Works

[edit]
  • Geometria analityczna w n wymiarach (1950) (translated to English as Multidimensional Analytic Geometry, Polish Scientific Publishers, 1969)
  • Podstawy geometrii (1955)
  • Foundations of Geometry (1960) with Wanda Szmielew, North Holland publisher[2]
  • Theory of Retracts (1967), PWN, Warszawa.
  • Theory of Shape (1975)
  • Collected papers vol. I, (1983), PWN, Warszawa.

See also

[edit]

References

[edit]
  1. ^ Karol Borsuk at the Mathematics Genealogy Project
  2. ^ Freudenthal, H. (1961). "Review: Foundations of geometry, Euclidean and Bolyai–Lobachevskian geometry, projective geometry. By K. Borsuk and Wanda Szmielew. Revised English translation" (PDF). Bull. Amer. Math. Soc. 67 (4): 342–344. doi:10.1090/s0002-9904-1961-10606-x.
[edit]
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