Karol Borsuk

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

Karol Borsuk
Born(1905-05-08)May 8, 1905
DiedJanuary 24, 1982(1982-01-24) (aged 76)
Alma materWarsaw University
Known forBorsuk's conjecture
Borsuk–Ulam theorem
Scientific career
Doctoral advisorStefan Mazurkiewicz
Notable students

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.

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, Jan Jaworowski, Krystyna Kuperberg, Włodzimierz Kuperberg, and Andrzej Trybulec.


  • 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.

See also


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