Ideas and influence of Karol Borsuk

• Autorzy: Dydak J.
• Konferencja: 6th European Congress of Mathematics, 2-7 July 2012 Kraków
• Języki publikacji: EN

Słowa kluczowe

EN

Borsuk Karol; mathematical work

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2012
• Tom: T. 48, Nr 2
• Strony: 81--95
• Opis fizyczny: Bibliogr. 45 poz.

Twórcy

autor

Dydak J.

• Department of Mathematics University of Tennessee Knoxville, TN 37996 USA

Bibliografia

• [l] K. Borsuk, Drei Sätze über die n-dimensionale euklidische Sphäre, Fund. Math. 20 (1933). 177-190.
• [2] K. Borsuk, On some metrizations of the hyperspace of compact sets, Fund. Math. 41 (1954), 168-202.
• [3] K. Borsuk, W. Szmielew, Foundations of Geometry, North Holland 1960.
• [4] K. Borsuk, Theory of Retracts, Polish Scientific Publishers, 1966.
• [5] K. Borsuk, Theory of shape, Lecture Notes Series, vol. 28, Aarhus Universitet 1971.
• [6] K. Borsuk, Theory of Shape, Polish Scientific Publishers 1975.
• [7] K. Borsuk, Collected papers, Polish Scientific Publishers, Warsaw 1983.
• [8] A. Deleanu, P. J. Hilton, On the categorical shape of a functor, Fund. Math. 97 (1977), 157-176.
• [9] A. Deleanu, P.J. Hilton, Borsuk's shape and Grothendieck categories of pro-objects, Math. Proc. Camb. Phil. Soc. 79 (1976), 473-482.
• [10] A. N. Dranishnikov, On a problem of P.S. Aleksandrov, Mat. Sb. 135 (1988), 551-557.
• [11] A. N. Dranishnikov, Homological dimension theory, Uspehi Mat. Nauk 43 (1988), 11-55.
• [12] J. Dydak,]. Segal, Shape theory. An introduction, Lecture Notes in Math., vol. 688, Springer Verlag 1978.
• [13] J. Dydak, Epimorphisms and monomorphisms in homotopy, Proc. Amer. Math. Soc. 116 (1992), 1171-1173.
• [14] J.Dydak, J.J.Walsh, Infinite dimensional compacta having cohomological dimension two: An application of the Sullivan Conjecture, Topology 32 (1993), 93-104.
• [15] E. Dyer, J. Roitberg, Homotopy-epimorphisms, homotopy-monomorphisms and homotopy-equivalences, Topology and its Applications 46 (1992), 119-124.
• [16] S. Eilenberg, Karol Borsuk - personal reminiscences, Topol. Methods Nonlinear Anal. 1 (1993), 1-2.
• [17] S. Ferry, Tfie homeomorphism group of a compact Q-manifold is an ANR, Bull. Amer. Math. Soc. 82 (1976), 910-912.
• [18] S. Ferry, Topological finiteness theorems for manifolds in Gromov-Hausdorff s[ace, Duke Mathematical Journal 74 (1994), 95-106.
• [19] R. Geoghegan, Topological methods in group theory, Graduate Texts in Mathematics, vol. 243, Springer Verlag 2007.
• [20] A. Granas, J. Jaworowski, Reminiscences of Karol Borsuk, Topol. Methods Nonlinear Anal. 1 (1993), 3-8.
• [21] K. Grove, P. Petersen, Bounding homotopy types by geometry, The Annals of Mathematics 128 (1988), 195-206.
• [22] P.Hilton, Duality in homotopy theory: a retrospective essay,]. Pure Appl. Algebra 19 (1980), 159-169.
• [23] P. Hilton, On some contributions of Karol Borsuk to homotopy theory, Topol. Methods Nonlinear Anal. 1 (1993), 9-14.
• [24] S.-T. Hu, Theory of retracts, Wayne State University Press 1965.
• [25] I. M. James (ed.), Topological Topics. Articles on Algebra and Topology Presented to Professor P J Hilton in Celebration of his Sixtieth Birthday, London Mathematical Society Lecture Note Series, vol. 86, 1983.
• [26] I. M. James (ed.), History of Topology, Elsevier Science 2006.
• [27] J. Kahn, G. Kalai, A counterexample to Borsuk's conjecture, Bulletin of the American Mathematical Society 29 (1993), 60-62.
• [28] D. Kołodziejczyk, There exists a polyhedron dominating infinitely many different homotopy types, Fund. Math. 151 (1996), 39-46.
• [29] K. M. Kuperberg, A smooth counterexample to the Seifert conjecture, Ann. of Math. 140 (1996), 723-732.
• [30] K. M. Kuperberg, W. Kuperberg, P. Mine, C. S. Reed, Examples Related to Ulam's Fixed Point Problem, Topol. Methods Nonlinear Anal. 1 (1993), 173-181.
• [31] S. Mardeśić, J. Segal, Shape theory, North-Holland Publ.Co., Amsterdam 1982.
• [32] J. Matoušek, Using the Borsuk–Ulam theorem, Springer Verlag, Berlin 2003.
• [33] M. Moszyńska, Karol Borsuk: 08.05.1905 – 24.01.1982, Glas. Mat. Ser. III 17 ( (1982), 413-423.
• [34] J. M.R. Sanjurjo, Shape and Conley Index of Attractors and Isolated Invariant Sets, vol. 75, Birkhauser Verlag, Basel/Switzerland 2007, Progress in Nonlinear Differential Equations and Their Applications.
• [35] J. M.R. Sanjurjo, Stability, attraction and shape: A topological study of flows, vol. 12, Juliusz Schauder Center winter school on topological methods in nonlinear analysis 2011, Lecture Notes in Nonlinear Analysis.
• [36] J. Segal, Borsuk's shape theory, Topol. Methods Nonlinear Anal. 1 (1993), no. 1, 43-48.
• [37] E. V. Shchepin, Finite-dimensional bicompact absolute neighborhood retracts are metrizable, Dokl.Akad.Nauk SSSR 233 (1977), 304-307.
• [38] K. Sieklucki, The scientific activity of Professor Karol Borsuk, Wiad. Mat. 20 (1978), 172-174. in Polish.
• [39] R. S. Simon, S. Spież, H. Toruńczyk, The existence of equilibria in certain games, separation for families of convex functions and a theorem of Borsuk-Ulam type, Israel Journal of Mathematics 92 (1995), 1-21.
• [40] H. Toruńczyk, Homeomorphism groups of compact Hilbert cube manifolds which are manifolds, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 25 (1977), 401-408.
• [41] W. Thurston, On proof and progress in mathematics, Bull. Am. Math. Soc. 30 (1994), 161-177.
• [42] S. M. Ulam, Adventures Of a mathematician, Charles Scribner's Sons, New York 1976.
• [43] O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, Elementary Topology Problem Textbook, AMS 2009.
• [44] J. West, Borsuk's influence on infinite-dimensional topology, Topol. Methods Nonlinear Anal. 1 (1993), no. 1, 35-41.
• [45] E. C. Zeeman, On the dunce hat, Topology 2 (1964), 341-358.