# Karol Borsuk

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

Karol Borsuk | |
---|---|

Born | |

Died | January 24, 1982 76) | (aged

Nationality | Polish |

Alma mater | Warsaw University |

Known for | Borsuk's conjecture Borsuk–Ulam theorem |

Scientific career | |

Fields | Mathematics |

Doctoral advisor | Stefan 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.

## Works

*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

- Bing–Borsuk conjecture
- Borsuk's conjecture
- Borsuk–Ulam theorem
- Zygmunt Janiszewski
- Stanislaw Ulam
- Scottish Café
- Animal Husbandry, an educational dice game published by Borsuk at his own expense in 1943 during the German occupation of Warsaw.

## References

- 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.

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