Karol Borsuk | Academic Influence

Karol Borsuk's AcademicInfluence.com Rankings

Karol Borsuk

Mathematics

#350

Historical Rank

Algebraic Topology

#14

Historical Rank

Topology

#18

Historical Rank

Measure Theory

#766

Historical Rank

mathematics Degrees

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Mathematics

Karol Borsuk's Degrees

PhD Mathematics University of Warsaw

Why Is Karol Borsuk Influential?

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According to Wikipedia, Karol Borsuk was a Polish mathematician. His main interest was topology, while he obtained significant results also in functional analysis. Borsuk introduced the theory of absolute retracts and absolute neighborhood retracts , 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; in particular, his open problems stimulated the infinite-dimensional topology.

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Karol Borsuk's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Theory Of Retracts (1967) (885)
Drei Sätze über die n-dimensionale euklidische Sphäre (1933) (555)
What is the theory of shape? (1980) (207)
On the imbedding of systems of compacta in simplicial complexes (1948) (201)
Concerning homotopy properties of compacta (1968) (183)
On symmetric products of topological spaces (1931) (128)
Fundamental retracts and extensions of fundamental sequences (1969) (74)
Sur les rétractes (1931) (62)
On some metrizations of the hyperspace of compact sets (1955) (60)
Multidimensional Analytic Geometry (1969) (59)
Sur la courbure totale des courbes fermées (1948) (59)
On movable compacta (1970) (55)
On a class of continuous mappings (1958) (41)
Some Remarks Concerning Topologically Homogeneous Spaces (1965) (36)
A note on the theory of shape of compacta (1970) (34)
On the third symmetric potency of the circumference (1949) (33)
Über eine Klasse von lokal zusammenhängenden Räumen (1932) (31)
Sur un continu acyclique qui se laisse transformer topologiquement en lui même sans points invariants (1935) (31)
Concerning the classification of topological spaces from the stand point of the theory of retracts (1959) (25)
Un théorème sur les prolongements des transformations (1937) (21)
Foundations of geometry : Euclidean and Bolyai-Lobachevskian geometry, projective geometry (1960) (21)
Some quantitative properties of shapes (1976) (21)
Quelques théorèmes sur les ensembles unicohérents (1931) (20)
Sur les prolongement des transformations continues (1937) (19)
Einige Sätze über stetige Streckenbilder (1932) (17)
An example of a simple arc in space whose projection in every plane has interior points (1947) (15)
On homotopy types of 2-dimensional polyhedra (1980) (15)
Sur un espace compact localement contractile qui n'est pas un rétracte absolu de voisinage (1948) (14)
SOME PROBLEMS IN THE THEORY OF SHAPE OF COMPACTA (1979) (14)
On a metrization of the hyperspace of a metric space (1977) (14)
On Several Problems of the Theory of Shape (1975) (13)
Über Schnitte dern-dimensionalen Euklidischen Räume (1932) (13)
On the Lusternik-Schnirelmann category in the theory of shape (1978) (11)
Some remarks concerning the shape of pointed compacta (1970) (11)
Über das Phänomen der Unzerlegbarkeit in der Polyedertopologie (1935) (10)
Zur kombinatorischen Eigenschaften der Retrakte (1933) (10)
Über stetige Abbildungen der euklidischen Räume (1933) (10)
Sur la somme et le produit combinatoire des rétractes absolus (1932) (10)
Quelques rétractes singuliers (1935) (10)
On the decomposition of a locally connected compactum into Cartesian product of a curve and a manifold (1953) (9)
On labil and stabil points (1952) (9)
On The Topology of Retracts (1947) (9)
Concerning the ordering of shapes of compacta (1970) (8)
A 3-dimensional absolute retract which does not contain any disk (1964) (8)
Concerning the set of retractions (1967) (8)
On the decomposition of manifolds into curves and surfaces (1945) (7)
Über die Abbildungen der metrischen kompakten Räume auf die Kreislinie (1933) (7)
On an irreducible 2-dimensional absolute retract (1950) (7)
On a Class of Compacta (7)
On a metrization of polytopes (1959) (7)
On embedding curves in surfaces (1966) (7)
Sur la décomposition des polyèdres en produits cartésiens (1938) (6)
A note on the shape of quasi-homeomorphic compacta (1970) (6)
Axioms of Incidency (1989) (6)
Errata to the paper "Fundamental retracts and extensions of fundamental sequences" Fundamenta Mathematicae 64 (1969), pp. 55-85 (1969) (5)
On. positions of sets in spaces. (1973) (5)
Concerning the Cartesian product of Cantor-manifolds (1951) (5)
Ensembles dont les dimensions modulaires de Alexandroff coïncident avec la dimension de Menger-Urysohn (1936) (5)
A countable broom which cannot be imbedded in the plane (1963) (5)
On the shape of the suspension (1970) (5)
Remarks on the homotopic join of maps (1961) (5)
Über den Lusternik-Schnirelmannschen Begriff der Kategorie (1936) (5)
SOME REMARKS ON COVERING OF BOUNDED SUBSETS OF THE EUCLIDEAN n-SPACE WITH SETS OF SMALLER DIAMETER (1978) (5)
Some remarks on shape properties of compacta (1974) (4)
Theory of shape : lectures, Fall 1970 (1971) (4)
Zur Dimensionstheorie der lokal zusammenziehbaren Räume (1934) (4)
Set theoretical approach to the disconnection theory of the Euclidean space (1950) (3)
Sur les transformations des polyèdres acycliques en surfaces sphériques (1937) (3)
Sur L'Addition Homologique des Types De Transformations Continues en Surfaces Spheriques (1937) (3)
Sur un problème de MM. Kuratowski et Ulam (1938) (3)
An example of a finite dimensional continuum having an infinite number of Cartesian factors (1951) (3)
ON A NEW SHAPE INVARIANT (1976) (3)
Sur un espace des transformations continues et ses applications topologiques (1931) (3)
Über stetige Abbildungen der Teilmengen euklidischer Räume auf die Kreislinie (1936) (2)
Two remarks concerning retracts of ANR-spaces (1967) (2)
Concerning the shapes of n-dimensional spheres (1974) (2)
On a problem of V. Klee concerning the Hilbert manifolds (1961) (2)
On fundamental deformation retracts and on some related notions (1975) (2)
Concerning the homological structure of the functional space (1952) (2)
An alternative concept of the n-dimensional measure (1983) (2)
Some remarks concerning the theory of shape in arbitrary metrizable spaces (1972) (2)
Über die Fundamentalgruppe der Polyeder im euklidischen dreidimensionalen Raume (1934) (2)
Ein Satz über Unikohärenz (1933) (2)
Über gewisse Invarianten der ε-Abbildungen (1933) (2)
Remarks on the n-dimensional geometric measure of compacta (1984) (2)
Remarques sur la quasi-homéomorphie (1958) (2)
Sur l'ensemble de valeurs qu'une fonction continue prend une infinité de fois (2)
Contribution à la topologie des polytopes (1935) (2)
Concerning the Euler characteristic of normal spaces (1948) (1)
Sur un problème de M. J. Schreier (1935) (1)
Sur la décomposition des courbes régulières en dendrites (1934) (1)
Concerning a problem due to Sam B. Nadler, Jr. (1976) (1)
On some hereditable shape properties (1974) (1)
Proceedings of the International Conference on Geometric Topology : Warszawa, August 24-September 2, 1978 (1980) (1)
On a family of 2-dimensional AR-sets (1962) (1)
Quelques relations entre la situation des ensembles et la rétraction dans les espaces euclidiens (1937) (1)
Sur le plongement des espaces dans les rétractes absolus (1936) (1)
Hopf's extension theorem in the theory of shape (1975) (1)
Correction à mon travail "Sur la courbure totale des courbes fermées" (1948) (1)
Grundlagen der Geometrie Vom Standpunkte der Allgemeinen Topologie Aus (1959) (1)
Families of compacta and some theorems on sweeping (1955) (1)
On covering of bounded sets by sets with the twice less diameter (1979) (1)
On a concept of dependence for continuous mappings (1956) (1)
On topological approximation of polytopes (1948) (0)
ON HOMOTOPY PROPERTIES OF COMPACT SUBSETS OF THE HILBERT SPACE (1972) (0)
Un théorème sur les groupes de Betti des ensembles localement connexes en toutes les dimensions ≤ n (1935) (0)
Sur la décomposition des continus péaniens plans (0)
On certain mapping of the 2-sphere onto itself (1952) (0)
Sur les transformations continues n'augmentant pas la dimension (1937) (0)
Contribution à l'étude des transformations essentielles (1938) (0)
Sur les coupures locales des variétés (1939) (0)
SOME REMARKS ON PERFORATED SPACES (1976) (0)
Dependence of mappings and equivalence of sets (1961) (0)
The theory of retracts and its problems (1964) (0)

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What Schools Are Affiliated With Karol Borsuk?

Karol Borsuk is affiliated with the following schools:

University of Warsaw

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