Karol Borsuk
Encyclopedia
Karol Borsuk was a Polish
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...

 mathematician.
His main interest was topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

.

Borsuk introduced the theory of absolute retracts (ARs) and absolute neighborhood retracts (ANRs), and the cohomotopy group
Cohomotopy group
In mathematics, particularly algebraic topology, cohomotopy sets are particular contravariant functors from the category of pointed topological spaces and point-preserving continuous maps to the category of sets and functions...

s, later called Borsuk-Spanier
Spanier
Spanier means "man from Spain" in German and may refer to as a surname:* Edwin Henry Spanier , known for the Alexander-Spanier cohomology theory* Graham Spanier, former president of Penn State University...

 cohomotopy groups. He also founded the so called Shape theory
Shape theory (mathematics)
Shape theory is a branch of the mathematical field of topology. Homotopy theory is not appropriate for spaces with bad local properties, hence the need for replacement of homotopy theory by a more sophisticated approach...

. 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
Master's degree
A master's is an academic degree granted to individuals who have undergone study demonstrating a mastery or high-order overview of a specific field of study or area of professional practice...

 and doctorate
Doctorate
A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder to teach in a specific field, A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder...

 from Warsaw University in 1927 and 1930, respectively; his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...

 thesis advisor was Stefan Mazurkiewicz
Stefan Mazurkiewicz
Stefan Mazurkiewicz was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning...

. He was a member of the Polish Academy of Sciences
Polish Academy of Sciences
The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

 from 1952. Borsuk's students included Samuel Eilenberg
Samuel Eilenberg
Samuel Eilenberg was a Polish and American mathematician of Jewish descent. He was born in Warsaw, Russian Empire and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor...

, Krystyna Kuperberg and Włodzimierz Kuperberg.

See also

  • Borsuk's conjecture
    Borsuk's conjecture
    The Borsuk problem in geometry, for historical reasons incorrectly called a Borsuk conjecture, is a question in discrete geometry.-Problem:...

  • Borsuk-Ulam theorem
  • Zygmunt Janiszewski
    Zygmunt Janiszewski
    Zygmunt Janiszewski was a Polish mathematician.-Life:His mother was Julia Szulc-Chojnicka. His father, Czeslaw Janiszewski, was a graduate of the University of Warsaw and was an important person in finance, being the director of the Société du Crédit Municipal in Warsaw.Janiszewski taught at the...

  • Stanislaw Ulam
  • Scottish Café
    Scottish Café
    The Scottish Café was the café in Lwów where, in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and topology....


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

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK