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Karol Borsuk (May 8, 1905, Warsaw – January 24, 1982, Warsaw) 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, Krystyna Kuperberg and Włodzimierz Kuperberg.
See also

Borsuk's conjecture
Borsuk-Ulam theorem
Zygmunt Janiszewski
Stanislaw Ulam
Scottish Café

Works

Geometria analityczna w n wymiarach (1950)
Podstawy geometrii (1955)
Foundations of Geometry (1960) with Wanda Szmielew, North Holland publisher
Theory of Retracts (1966)
Theory of Shape (1975)

External links

O'Connor, John J.; Robertson, Edmund F., "Karol Borsuk", MacTutor History of Mathematics archive, University of St Andrews.
Karol Borsuk at the Mathematics Genealogy Project

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