Karol Borsuk

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Karol Borsuk
Born (1905-05-08)May 8, 1905
Warsaw, Poland, Russian Empire
Died January 24, 1982(1982-01-24) (aged 76)
Warsaw, Poland
Nationality Polish
Fields Mathematics
Alma mater Warsaw University
Doctoral advisor Stefan Mazurkiewicz
Notable students Samuel Eilenberg, Andrzej Granas, Jan Jaworowski, Hanna Patkowska, Włodzimierz Kuperberg, Krystyna Kuperberg, Henryk Toruńczyk (mathematician)
Known for Borsuk's conjecture
Borsuk–Ulam theorem

Karol Borsuk (May 8, 1905 – January 24, 1982) was a Polish mathematician. His main interest was topology.

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 the so-called 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.

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, Andrzej Granas, Jan Jaworowski, Hanna Patkowska, Krystyna Kuperberg, Włodzimierz Kuperberg, Henryk Toruńczyk, Włodzimierz Holsztyński, Andrzej Trybulec and Jerzy Dydak,

See also


  • 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[1]
  • Theory of Retracts (1967), PWN, Warszawa.
  • Theory of Shape (1975)
  • Collected papers vol. I, (1983), PWN, Warszawa.


External links