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

var GLB_RIS='http://www.economicexpert.com';var GLB_RIR='/cincshared/external';var GLB_MMS='http://www.economicexpert.com';var GLB_MIR='/site/image';GLB_MML='/'; document.write(''); document.write(''); document.write(''); document.write(''); A1('s',':','html'); Non User A B C ... 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 John Vincent Atanasoff Bulgarian Bosnian ... Bosnian (Zbigniew Brzezinski) - Pole Mikhail Bulgakov Russian Ivan Bunin ... Fryderyk Chopin (Frederic Chopin) - Pole Boris Christoff Bulgarian Grigori Chukhrai ... Russian (Nicolaus Copernicus) - Pole Vladimir Dal Russian Danish ... Czech , raised in Switzerland Jan Hus Czech Bosniak ... Croat mother), born and raised in Sweden Croat Jaromir Jagr Czech Matija Jama Slovenian Milla Jovovich Serbo Russian ... Pole (Krzysztof Kieslowski) - Pole Velimir Khlebnikov Russian Andrey Kolmogorov ... Russian Jernej Kopitar Slovenian Sergei Korolev Ukrainian (Thaddeus Kosciuszko) - Pole Stefka Kostadinova Bulgarian Croat ... Russian (Stanislaw Lem) - Pole Ivan Lendl Czech Vladimir Ilyich Lenin ... Belarusian (Witold Lutoslawski) - Pole Rudolf Maister Slovenian Manuela Maleeva ... Serb (Czeslaw Milosz) - Pole Alphonse Mucha Czech Bosnian ... Jewish ancestry) Croat Ivan Petrovich Pavlov Russian Anna Pavlova ... Serb father) (Jozef Pilsudski) - Pole Josip Plemelj Slovenian (Roman Polanski) - Pole Pope John Paul II Pole Alexander Popov ... Russian (Casimir Pulaski) - Pole Mihajlo Pupin Serb Aleksandr Pushkin ... Russian (Wladyslaw Reymont) - Pole Nikolai Rimsky-Korsakov Russian Franc Rozman Stane ... King Samo - unknown

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

Journals Home Search Author Info Subscribe ... Help 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 Welcome to J. F. Ptak Books, Maps, and Prints. We offer an extensive selection of rare scientific books, including thousands of mathematic texts, and books related to logic, the history of logic, computer science, and chaos theory. You will be redirected to our mathematics listings in 10 seconds. If your browser does not automatically redirect you in a few seconds, use the navigation bar at the top of this page to browse our store or click on this link to view our mathematics listings.

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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