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         Borsuk Karol:     more detail
  1. Theory of Retracts by Karol borsuk, 1967
  2. Theory of Shape. Monografie Matematyczne Tom 59 by Karol Borsuk, 1975-06
  3. Proceedings of the International Conference on Geometric Topology, Warszawa, August 24-September 2, 1978
  4. Oeuvres Choisies. Redigees par Karol Borsuk, Jan Jaworowski, Bronislaw Knaster et Kasimierz Kuratowski by Zygmunt Janiszewski, 1962-01-01
  5. Karol Borsuk: An entry from Gale's <i>Science and Its Times</i>
  6. Foundations of Geometry: Euclidean, Bolyal-Lobachevskian, Projective by karol; szmielew, Wanda borsuk, 1960
  7. MULTIDIMENSIONAL ANALYTIC GEOMETRY by Karol Borsuk, 1969-01-01
  8. Foundations of Geometry: Euclidean, Bolyai-Lobachevskian & Projective by Karol & SZMIELEW,Wanda BORSUK, 1957
  9. Collected papers by Karol Borsuk, 1983
  10. Theory of shape: Lectures, fall, 1970 (Lecture notes series) by Karol Borsuk, 1973
  11. Theory of shape (Monografie matematyczne) by Karol Borsuk, 1975
  12. Multidimensional analytic geometry (Polska Akademia Nauk. Institut matematyczny. Monografie matematyczne, v. 50) by Karol Borsuk, 1969

41. TMNA - Volume 1 Number 1
item, Reminiscences of karol borsuk A. Granas and J. Jaworowski. 3. item, On SomeContributions of karol borsuk to Homotopy Theory P. Hilton
http://www.tmna.ncu.pl/htmls/archives/vol-1-1.html
T OPOLOGICAL M ETHODS
IN
N ONLINEAR A NALYSIS
Vol. 1, No. 1 March 1993
TABLE OF CONTENTS Title and Author(s) Page Karol Borsuk Personal Reminiscences
S. Eilenberg Reminiscences of Karol Borsuk
A. Granas and J. Jaworowski On Some Contributions of Karol Borsuk to Homotopy Theory
P. Hilton Spheres and Symmetry: Borsuk's Antipodal Theorem
H. Steinlein Borsuk's Influence on Infinite-Dimensional Topology
J. West Borsuk's Shape Theory
J. Segal Subharmonic Solutions for Second Order Differential Equations A. Fonda, M. Ramos and M. Willem Global Bifurcation of Periodic Solutions K. Geba and W. Marzantowicz Existence Principles for Caratheodory Differential Equations in Banach Spaces M. Frigon and J. W. Lee Periodic Solutions of Some Semilinear Wave Equations on Balls and on Spheres A. K. Ben-Naoum and J. Mawhin Generic Domain Dependence for Non-smooth Equations and the Open Set Problem for Jumping Nonlinearities E. N. Dancer Deformation Properties for Continuous Functionals and Critical Point Theory J.-N. Corvellec, M. Degiovanni and M. Marzocchi Examples Related to Ulam's Fixed Point Problem K. M. Kuperberg, W. Kuperberg, P. Minc and C. S. Reed

42. 54: General Topology
MR3,318d; borsuk, karol; Dydak, Jerzy What is the theory of shape? , Bull.Austral. Math. Soc. 22 (1980), no. 2, 161198. MR82d54015; borsuk, K. What
http://www.math.niu.edu/~rusin/known-math/index/54-XX.html
Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields
POINTERS: Texts Software Web links Selected topics here
54: General topology
Introduction
More formally, a topological space is a set X on which we have a topology a collection of subsets of X which we call the "open" subsets of X. The only requirements are that both X itself and the empty subset must be among the open sets, that all unions of open sets are open, and that the intersection of two open sets be open. This definition is arranged to meet the intent of the opening paragraph. However, stated in this generality, topological spaces can be quite bizarre; for example, in most other disciplines of mathematics, the only topologies on finite sets are the discrete topologies (all subsets are open), but the definition permits many others. Thus a general theme in topology is to test the extent to which the axioms force the kind of structure one expects to use and then, as appropriate, introduce other axioms so as to better match the intended application. For example, a single point need not be a closed set in a topology. Does this seem "inappropriate"? Then perhaps you are envisioning a special kind of topological space, say a a metric space. This alone still need not imply the space looks enough like the shapes you may have seen in a textbook; if you really prefer to understand those shapes, you need to add the axioms of a manifold, perhaps. Many such levels of generality are possible.

43. Karol Adamiecki Harmony Management Importance Production
karol Adamiecki was one of the most famous management researchers in Central andEastern Europe in his karol borsuk karol J. Bobko Károly Németh
http://www.economicexpert.com/a/Karol:Adamiecki.htm
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Home
Karol Adamiecki ) was a Polish economist engineer and management researcher. Professor of Politechnika Warszawska . Founder and first director ( ) of Instytut Naukowej Organizacji in Warsaw . Vicepresident of European Association of Scientific Management (pl. Europejskie Stowarzyszenie Naukowego Zarzadzania Karol Adamiecki was one of the most famous management researchers in Central and Eastern Europe in his times. He begun his research in Petersburg Russia , then moved to Poland He did majority of his research and observation in the metallurgy area. He is the author of the law of harmony in management - harmony should be composed of three parts:
  • harmony of choice (all production tools should be compatible with each other, with special regard to their output production speed) harmony of doing (importance of time coordination, schedules and harmonogram s)

44. Karol Borsuk Biography
karol borsuk biography and related resources. licensed under the GNU FreeDocumentation License. It uses material from the Wikipedia article karol borsuk.
http://www.biographybase.com/biography/Borsuk_Karol.html
Biography Base Home Link To Us Search Biographies: Browse Biographies A B C D ... Z Karol Borsuk Biography Karol Borsuk (May 8, 1905 - January 24, 1982) was a Polish mathematician born in Warsaw. He received his master's degree and doctorate from Warsaw University in 1927 and 1930, respectively.
His main interest was topology. See Borsuk-Ulam theorem. Karol Borsuk Resources Contact Us Sitemap
This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article Karol Borsuk

45. Irzykowski, Karol --  Encyclopædia Britannica
karol borsuk University of St.Andrews, Scotland Brief note on the life and worksof this Polish mathematician known for his contributions to topology.
http://www.britannica.com/eb/article?tocId=9042832

46. ErdosA, Version 2004, February 2, 2004 This Is A List Of All
ITSHAK Borovik, Alexandre Vasilievich Borowiecki, Mieczyslaw Borsik, Jan Borst,Sem C. borsuk, karol Borwein, David Borwein, Jonathan Michael Borwein,
http://www.oakland.edu/enp/ErdosA
ErdosA, Version 2004, February 2, 2004 This is a list of all persons with Erdos number less than or equal to 2, including Paul Erdos, 509 people with Erdos number 1, and 6984 people with Erdos number 2. An asterisk following the name indicates that this Erdos co-author is known to be deceased; additional information about the status of Erdos co-authors would be most welcomed. (This convention is not used for those with Erdos number 2, as to do so would involve too much work.) Please send corrections and comments to . The Erdos Number Project Web site can be found at the following URL:

47. Erdos2, Version 2004, February 2, 2004 This Is A List Of The 6984
Translate this page TIBOR Borst, Sem C. WINKLER, PETER M. borsuk, karol ULAM, STANISLAW MARCIN*Borwein, David MEIR, AMRAM Borwein, Jonathan Michael PREISS, DAVID RICHMOND,
http://www.oakland.edu/enp/Erdos2
Erdos2, Version 2004, February 2, 2004 This is a list of the 6984 persons with Erdos number equal to 2, together with their co-authors who have Erdos number 1 listed beneath them. An asterisk following the name indicates that this Erdos co-author is known to be deceased; additional information about the status of Erdos co-authors would be most welcomed. (This convention is not used for those with Erdos number 2, as to do so would involve too much work.) Please send corrections and comments to . The Erdos Number Project Web site can be found at the following URL:

48. MIMUW - Karol Sieklucki
Sieklucki, karol The scientific activity of Professor karol borsuk, Wiadom. Sieklucki, karol A generalization of the borsuk theorem on antipodal points,
http://www.mimuw.edu.pl/english/research/imat-publications/siekluck.html
 Only in this directory English Pomoc Jak trafiæ? Zajêcia ... Institute of Mathematics faculty members publications
Karol Sieklucki
List of Publications
Engelking, R.; Sieklucki, Karol
Topology: a geometric approach,
Sigma Series in Pure Mathematics . Heldermann Verlag, Berlin, 1992. x+429 pp. Engelking, R.; Sieklucki, Karol
Wstêp do topologii,
Biblioteka Matematyczna . PWN, Warsaw, 1986. 459 pp. Sieklucki, Karol; Sobolewski, M.
On a generalization of a theorem of Lokucievski,
Bull. Polish Acad. Sci. Math. (1985), no. 11-12, pp.637-643. Sieklucki, Karol
Generalized cones and the fixed point property,
Bull. Polish Acad. Sci. Math. (1985), no. 3-4, pp.173-176. Sieklucki, Karol
Borsuk, Karol Collected papers. Part I, II. With introductory material by Karol Sieklucki and S³awomir Nowak,
PWN-Polish Scientific Publishers, Warsaw, 1983. xxiv+1357 pp. (1 plate). Sieklucki, Karol An inductive proof of the nonretractibility of a cell onto its boundary, Prace Mat. (1983), no. 1, pp.129-131. Sieklucki, Karol The fixed point property for 1-dimensional continua, Proceedings of the International Conference on Geometric Topology (Warsaw, 1978), pp.409-410, PWN, Warsaw, 1980.

49. Bibliography
borsuk, karol, 19051982, Collected papers karol borsuk, Warszawa, PWN / olishScientific Publishers, 1983. Bossut, Charles, 1730-1814
http://www.library.cornell.edu/math/bibliography/display.cgi?start=B&

50. Bibliography
Janiszewski, Zygmunt, 18881920, Oeuvres choisies / redigees par karol borsuk etal. Warszawa, Panstowowe Wydawn. Naukowe, 1962
http://www.library.cornell.edu/math/bibliography/display.cgi?start=J&

51. Warsaw University: Information From Answers.com
Czeslaw RyllNardzewski Wladyslaw Taczanowski Warsaw University of Technology Warsaw Agricultural University Tadeusz Banachiewicz karol borsuk
http://www.answers.com/topic/warsaw-university
showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Best of Web Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Warsaw University Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); Warsaw University
Warsaw University Data Polish Uniwersytet Warszawski Latin Universitas Varsoviensis Established November 19 Location Warsaw Poland EU Enrolment 60 844 (November Rector Address
Warsaw

Poland
Phone E-mail Homepage Warsaw University http://www.uw.edu.pl Membership EUA Socrates-Erasmus Map
Warsaw in Poland
Warsaw University Polish Uniwersytet Warszawski ) - the biggest and one of the most prestigious universities in Poland
History
The Royal University of Warsaw was established in , when the partitions of Poland separated Warsaw from the oldest and most influential academic center in Cracow . The School of Law and the Medical School were first established in the Duchy of Warsaw . In Alexander I permitted the Polish authorities to create a university, composed of five faculties: Law and Administration, Medicine, Philosophy, Theology and Art and Humanities. Soon the university grew and the number of students reached 800 while the number of professors reached 50.

52. List Of Slavs: Information From Answers.com
karol borsuk Pole Mark Bosnich - Croat-Australian Goran Bregovic - Bosnian Zbigniew Brzezinski (Zbigniew Brzezinski) - Pole Mikhail Bulgakov
http://www.answers.com/topic/list-of-slavs
showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping List of Slavs Wikipedia @import url(http://content.answers.com/main/content/wp/css/common.css); @import url(http://content.answers.com/main/content/wp/css/gnwp.css); List of Slavs This is a list of famous Slavic people

53. Karol Borsuk On The Homotopy Types Of Some
karol borsuk On the Homotopy Types of Some Decomposition Spaces Bull. de L Acad. Pol., ser. math.,astr.et phys., XVIII, 5,
http://www.cs.ualberta.ca/~piotr/Mizar/History/CATM/BORSUK/BORSUK.MIZ
as Element of X#Y; end; priority 15: ^; priority 14: sp proj; priority 13: the_carrier_of; priority 12: Id OMEGA; definition let X be set; func Id X -> Function of X,X; end; definition let X1,X2,Y1,Y2 be set, F be (Function of X1,X2), G be Function of Y1,Y2; func F#G ->Function of X1#Y1,X2#Y2; end; TM11: for X,Y,Z for F being (Function of X,Y), x being (Element of X), z being Element of Z holds (F#Id Z). ; TM12: for X,Y,Z for F being (Function of X,Y), y being (Element of Y), z being Element of Z holds (F#Id Z)" = (F"y)#z; TM13: for X,Y,Z for F being (Function of X,Y), A being (Subset of X), B being Subset of Z holds (F#Id Z).(A#B) = (F.A)#B; TM0: for x,x', y,y' being Any st = (e ofhC be set, .(F.A)=(G.F).A; TM3: for X,Y fU set, A be (Subset of XB x bDecomporedefine fU i o l o lds (F#Id Z)(e ofTC1 XT set, Afor F bein#Yine fY bproduct of X and the sT set, Afor F beiY x beT= (e ofTC1' XT set, A holds (F#Id Z).

54. Central Archive Of Mizar Texts (Mizar-4)
borsuk 198707-03. Andrzej Trybulec s formalization of On the Homotopy Types ofSome Decomposition Spaces by karol borsuk, Bull. de L Acad.
http://www.cs.ualberta.ca/~piotr/Mizar/History/CATM/
Central Archive of Mizar Texts (Mizar-4)
Note: Mizar-4 used ASCII IBM Set II. Because some of the characters cannot be easily rendered in a textfile, a poststript version of each article is provided. 1988-09-22
  • BORSUK Andrzej Trybulec's formalization of On the Homotopy Types of Some Decomposition Spaces by Karol Borsuk, Bull. de L'Acad. Pol., ser. math.,astr.et phys., XVIII, 5, 1970
  • HEYTING Andrzej Trybulec, Algebra of Normal Forms
  • H. Oryszczyszyn, M. Prazmowska, K. Prazmowski, Elements of ordered affine geometry, in 6 parts (descriptions in Polish)
  • Edmund Woronowicz, Application of Mizar 4 to the proof of transformation conditions for specified programs. An example.
  • TEORMN Stanislaw T. Czuba, Elementary property of sets (description in Polish)
  • Stanislaw T. Czuba, Elementary topological properties, Part I and II, (descriptions in Polish)
  • IND Stanislaw T. Czuba, Application of mathematical induction, an example (description in Polish)
  • ARYTHM INDUC Grzegorz Bancerek's, Theoretical arithmetic (based on Zarys arytmetyki teoretycznej by Andrzej Grzegorczyk.

55. Bulletin Of The American Mathematical Society
Bor borsuk, karol, and Wanda Szmielew, Foundations of geometry Euclidean andBolyaiLobachevskian geometry. Projective geometry, New York Interscience
http://www.ams.org/bull/2002-39-04/S0273-0979-02-00949-7/home.html

ISSN 1088-9485(e) ISSN 0273-0979(p) Previous issue Table of contents Next issue
Articles in press
... All issues Book Review The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.
Retrieve article in: PDF DVI TeX PostScript Book Information
Author(s): Robin Hartshorne.
Title: Geometry: Euclid and beyond
Additional book information: Springer-Verlag, New York, 2000, xi+526, $49.95, 0-387-98650-2 References:
[Bis]
Bishop, Errett, and Douglas Bridges, Constructive Analysis , New York: Springer-Verlag, 1985. MR
[Bor]
Borsuk, Karol, and Wanda Szmielew, Foundations of geometry: Euclidean and Bolyai-Lobachevskian geometry. Projective geometry , New York: Interscience Publishers, 1960. MR
[CoWe]
Cornish, Neil J., and Jeffrey R. Weeks, ``Measuring the Shape of the Universe", Notices of the AMS MR
[Efi]
Efimov, N. V., ``Generation of singularities on surfaces of negative curvature" [Russian]

56. Chronology Of Pure And Applied Mathematics
1933, karol borsuk and Stanislaw Ulam present the borsukUlam antipodal-pointtheorem. 1942, GC Danielson and Cornelius Lanczos develop a fast Fourier
http://www.3rd1000.com/chronology/chrono23.htm
Chronology of Pure and Applied Mathematics Egyptian mathematicians employ primitive fractions. Pythagoras studies propositional geometry and vibrating lyre strings. Eudoxus states the method of exhaustion for area determination. Aristotle discusses logical reasoning in Organon. Euclid studies geometry as an axiomatic system in Elements and states the law of reflection in Catoptrics. Archimedes computes pi to two decimal places using inscribed and cirumscribed polygons and computes the area under a parabolic segment. Apollonius writes On Conic Sections and names the ellipse, parabola, and hyperbola. Diophantus writes Arithmetica, the first systematic treatise on algebra. Tsu Ch'ung-Chih and Tsu Keng-Chih compute pi to six decimal places. Hindu mathematicians give zero a numeral representation in a positional notation system. Leonardo Fibonacci demonstrates the utility of Arabic numerals in his Book of the Abacus. Ghiyathal-Kashi computes pi to sixteen decimal places using inscribed and cirumscribed polygons. Scipione Ferro develops a method for solving cubic equations.

57. Pub
Topology Conference in honor of Kazimierz Kuratowski and karol borsuk, WarsawUniversity and the Institute of Mathematics of Polish Academy of Sciences,
http://www.auburn.edu/~kuperkm/talk.html
Selected conference lectures: International Symposium in Honour of Samuel Eilenberg, Torun, Poland, June 1993. Maryland-Penn State Regional Conference on Dynamical Systems and Related Topics, Maryland, March 1994. Topology Fest, Cornell University, Ithaca, New York, May 1994. Topology and Dynamical System Conference, Amsterdam, the Netherlands, August, 1994. American Mathematical Society Meeting, AMS Invited Lecture, Orlando, Florida, March 1995. Dynamical Systems Conference, Montevideo, Uruguay, March 1995. Banach Center Symposium on Ergodic Theory and Dynamical Systems, Warsaw, Poland, June 1995. 'Geometrie Complexe et Systemes Dynamiques' conference in honor of Adrien Douady, Orsay, France, July 1995. 'Dynamische Systeme' Conference, Oberwolfach, Germany, July 1995. Joint Mathematics Annual Meeting, MAA Invited Lecture, Orlando, Florida, January 1996. Topology Conference: in honor of Kazimierz Kuratowski and Karol Borsuk, Warsaw University and the Institute of Mathematics of Polish Academy of Sciences, Warsaw, Poland, May 1996. 'Dynamische Systeme' Conference, Oberwolfach, Germany, July 1997.

58. Eagle Bookshop - View Bookshelf
borsuk, karol, Collected Papers, parts 1 11, 1983, £50.00. Chung, Kai Lai,PAOLU HSU COLLECTED PAPERS, 1983, £38.00
http://eaglebookshop.hostinguk.com/BookShelf.aspx?bc=15&BookShelf=178

59. J.F.Ptak Books, Maps, And Prints Mathematics
borsuk,karol,Foundations of Geometry, borsuk,karol,Foundations of Geometry, Eichler,M.,Quadratische Formen und Orthogonale Gruppen, borsuk,karol
http://www.thesciencebookstore.com/books/mathematics/
Home Page About Us Books Prints and Maps ... Free Stuff
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60. A Borsuk Theorem On Homotopy Types
1 karol borsuk. On the homotopy types of some decomposition spaces. 2karol borsuk. \em Theory of Shape, volume 59 of \em Monografie Matematyczne.
http://mizar.uwb.edu.pl/JFM/Vol3/borsuk_1.html
Journal of Formalized Mathematics
Volume 3, 1991

University of Bialystok

Association of Mizar Users
A Borsuk Theorem on Homotopy Types
Andrzej Trybulec
Warsaw University, Bialystok
Summary.
We present a Borsuk's theorem published first in [ ] (compare also [ 2, pages 119-120 ]). It is slightly generalized, the assumption of the metrizability is omitted. We introduce concepts needed for the formulation and the proofs of the theorems on upper semi-continuous decompositions, retracts, strong deformation retract. However, only those facts that are necessary in the proof have been proved.
MML Identifier:
The terminology and notation used in this paper have been introduced in the following articles [
Contents (PDF format)
  • Preliminaries
  • Partitions
  • Topological Preliminaries
  • Cartesian Product of Topological Spaces
  • Partitions of Topological Spaces
  • Upper Semicontinuous Decompositions
  • Borsuk's Theorems on the Decomposition of Retracts
    Bibliography
    3] Leszek Borys. Paracompact and metrizable spaces Journal of Formalized Mathematics
    4] Czeslaw Bylinski. Basic functions and operations on functions Journal of Formalized Mathematics
    5] Czeslaw Bylinski.
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