Karol Borsuk

Who was Karol Borsuk?

Karol Borsuk was a Polish mathematician. His main interest was topology.

Borsuk introduced the theory of absolute retracts and absolute neighborhood retracts, 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, Jan Jaworowski, Krystyna Kuperberg, Włodzimierz Kuperberg, Andrzej Trybulec, Włodzimierz Holsztyński and Jerzy Dydak.