Topics in infinite dimensional topology

Andrzej Granas

Séminaire Jean Leray (1969-1970)

  • Issue: 3, page 1-131

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Granas, Andrzej. "Topics in infinite dimensional topology." Séminaire Jean Leray (1969-1970): 1-131. <http://eudml.org/doc/112546>.

@article{Granas1969-1970,
author = {Granas, Andrzej},
journal = {Séminaire Jean Leray},
language = {eng},
number = {3},
pages = {1-131},
publisher = {Collège de France},
title = {Topics in infinite dimensional topology},
url = {http://eudml.org/doc/112546},
year = {1969-1970},
}

TY - JOUR
AU - Granas, Andrzej
TI - Topics in infinite dimensional topology
JO - Séminaire Jean Leray
PY - 1969-1970
PB - Collège de France
IS - 3
SP - 1
EP - 131
LA - eng
UR - http://eudml.org/doc/112546
ER -

References

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  1. [1] R.F. Arens and J. Eells, Jr., On embedding uniform and topological spaces, Pacific J. Math., 6 (1956), 397-403. Zbl0073.39601MR81458
  2. [2] M. Artin and B. Mazur, On periodic points, Ann. of Math.81 (1965), 82-99. Zbl0127.13401MR176482
  3. [3] G.D. Birkhoff and O.D. Kellogg, Invariant points in function spaces, Trans. Amer. Math., Soc.23 (1922). Zbl48.0472.02MR1501192JFM48.0472.02
  4. [4] H.F. Bohnenblust and S. Karlin, On a theorem of Ville, Contributions to the theory of games, vol. I, Annals of Hath. Studies, Princeton, 1950. Zbl0041.25701MR41415
  5. [5] K. Borsuk, Sur un continu acyclique qui se laisse transformer topologiquement en lui-même sans points invariants, Fund. Math., 24 (1934), 51-58. Zbl0010.13402
  6. [6] — Theory of retracts, PWN, Warszawa, 1967. Zbl0153.52905
  7. [7] C. Bowszyc, Fixed point theorems for the pairs of spaces, BAPS16 (1968), 845-850. Zbl0177.51702MR246290
  8. [8] — On the Euler-Poincaré characteristic of a map and the existence of periodic points, Bull. Acad. Polon, Sci.17 (1969), 367-372. Zbl0177.51703MR253327
  9. [9] — Some theorems in the Theory of Fixed Points, (Thesis), University of Warsaw (1969) (in polish). 
  10. [10] D.G. Bourgin, Un indice dei punti, I, II, Atti. Acad. Naz. Lincei8, 19 (1955), 435-440, 20 (1956), 43-48. Zbl0073.39706
  11. [11] — Fixed points on neighbourhood retracts, Revue Math. Pures Appl.2, Hommage à S. Stoilow (1957), 371-374. Zbl0089.38904MR94785
  12. [12] F.E. Browder, On the fixed point index for continuous mappings of locally connected spaces, Summa Bras. Math.4 (1960), 253-293. Zbl0102.37901MR146834
  13. [13] — Fixed point theorems on infinite dimensional manifolds, Trans. Am. Math. Soc.119, 2 (1965), 179-194. Zbl0132.18803MR195082
  14. [14] A. Deleanu, Théorie des points fixes: sur les rétractes de voisinage des espaces convexoïdes, Bull. Soc. Math. Fr., 87 (1959), 235-243. Zbl0093.36801MR143203
  15. [15] A. Dold, Fixed point index and fixed point theorem for Euclidean neighbourhood retracts, Topology, 4 (1965), 1-8. Zbl0135.23101MR193634
  16. [16] J. Dugundji, An extension of Tietze's theorem, Pacific Journ. Math.1 (1951). Zbl0043.38105MR44116
  17. [17] S. Eilenberg and D. Montgomery, Fixed point theorems for multi-valued transformation, Amer. Journ. of Math.58 (1946), 214-222. Zbl0060.40203MR16676
  18. [18] Ky Fan, Fixed-point and minimax theorems in locall convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A.38 (1952), 121-126. Zbl0047.35103MR47317
  19. [19] F.B. Fuller, The existence of periodic points, Ann. of Math.57 (1953), 229-230. Zbl0050.17203MR52764
  20. [20] A. Gmurczyk, On approximative retracts, Bull. Acad. Polon. Sci.16 (1968), 9-14. Zbl0153.53102MR227916
  21. [21] L. Górniewicz and A. Granas, Fixed point theorems for multi-valued mappings of the absolute neighbourhood retracts, (to appear). Zbl0203.25203MR285004
  22. [22] A. Granas, Sur la notion du degré topologique pour une certaine classe de transformations multivalentes dans les espaces de Banach, Bull. Acad. Polon. Sci.7 (1959), 181-194. Zbl0087.32303MR108743
  23. [23] — Theorem on antipodes and theorems on fixed points for a certain class of multi-valued mappings in Banach spaces, Bull. Acad. Polon. Sci.7 (1959), 271-275. Zbl0089.11202MR117588
  24. [24] — Generalizing the Hopf-Lefschetz fixed point theorem for non-compact ANR-s, Symposium on Infinite Dimensional Topology, Bâton-Rouge, 1967. Zbl0235.55008
  25. [25] — Fixed point theorems for the approximative ANR-s, Bull. Acad. Polon. Sci.16 (1968), 15-19. Zbl0153.53201MR227917
  26. [26] — Some theorems in fixed point theory. The Leray-Schauder Index and the Lefschetz Number, Bull. Acad. Polon. Sci.17 (1969), 131-137. Zbl0185.51204MR246284
  27. [27] A. Granas and J.W. Jaworowski, Some theorems on multi-valued mappings of subsets of the Euclidean space, Bull. Acad. Polon. Sci.7 (1959), 277-283. Zbl0089.17902MR120627
  28. [28] H. Hopf, Eine Verallgemeinerung der Euler-Poincaréschen Formel, Nachr. Ges. Wiss., Göttingen (1928). Zbl54.0610.02JFM54.0610.02
  29. [29] M. Hukuhara, Sur l'application semi-continue dont la valeur est un compact convexe, Funkcialaj Ekvacioj10 (1967), 43-66. Zbl0155.19402MR222856
  30. [30] J.W. Jaworowski, Theorems on antipodes for multi-valued mappings and a fixed point theoren, Bull. Acad. Polon. Sci.4 (1956), 187-192. Zbl0074.38305MR79270
  31. [31] — Some consequences of the Vietoris Mapping Theorem, Fund. Math.45 (1958), 261-272. Zbl0080.38102
  32. [32] S. Kinoshita, On some contractible continua without fixed point property, Func. Math.49 (1953), 96-98. Zbl0053.12503MR60225
  33. [33] A. Lasota, Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci.13 (1965), 781-786. Zbl0151.10703MR196178
  34. [34] — Fixed-point theorems for multi-valued mappings and optimal control problemsBull. Acad. Polon. Sci.16 (1968), 645-649. Zbl0165.43304MR248580
  35. [35] S. Lefschetz, Intersections and transformations of complexes and manifolds, Trans. Amer. Math. Soc.28 (1926), 1-49. Zbl52.0572.02MR1501331JFM52.0572.02
  36. [36] — On locally-connected and related sets, Annals of Math.35 (1934), 118-129. Zbl0009.08603MR1503148JFM60.1218.01
  37. [37) J. Leray, Sur les équations et les transformations, J. Math. Pures Appl.24 (1945), 201-248. Zbl0060.40705MR15788
  38. [38] — La théorie des points fixes et ses applications en analyse, Proc. Int. Math. Congress, Cambridge1950, vol. 2, 202-208. Zbl0049.08803MR47318
  39. [39] — Théorie des points fixes : indice total et nombre de Lefschetz, Bull. Soc. Math. Fr.87 (1959), 221-233. Zbl0093.36702MR143202
  40. [40] — Fixed point index and Lefschetz number, Proc. Symp. on Infin. Dimen. Topology, Bâton-Rouge (1967). Zbl0235.55007
  41. [41] J. Leray et J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup.51 (1934). Zbl0009.07301JFM60.0322.02
  42. [42] M. Nagumo, Degree of mapping in convex linear topological spaces, Am. J. Math.73 (1951), 497-511. Zbl0043.17801MR42697
  43. [43] H. Noguchi, A generalization of absolute neighbourhood retracts, Kodai Math. Seminar Reports1 (1953), 20-22. Zbl0052.18803MR56279
  44. [44] J. Schauder, DerFixpunktsaztz in Funktionalräumen, Studia Math.2 (1930). JFM56.0355.01
  45. [45] E.H. Spanier, Algebraic Topology, Mc Graw Hill (1966). Zbl0145.43303MR210112
  46. [46] L. Vietoris, Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann.97 (1927), pp. 454-472. Zbl53.0552.01MR1512371JFM53.0552.01
  47. [1] P. Alexandroff, Dimensionstheorie. Ein Beitrag zur Geometrie der abgeschlossenen Mengen, Math. Ann.106 (1932), pp. 161-238. Zbl58.0624.01MR1512756JFM58.0624.01
  48. [2] K. Geba, Algebraic topology methods in the theory of compact fields in Banach spaces, Fund. Math.54 (1964), pp. 177-209. Zbl0128.36003MR162117
  49. [3] K. Geba and A. Granas, Algebraic topology in linear normed spaces I - V, Bull. Acad. Polon. Sci., I, 13 (1965), pp. 287-290; II, 13 (1965), pp. 341-346; III, 15 (1967), pp. 137-143; IV, 15 (1967), pp. 145-152; V, 17 (1969), pp. 123-130. Zbl0128.36101
  50. [4] K. Geba and A. Granas, On cohomology theory in linear normed spaces, Proc. Infinite Dimensional Topology, Baton Rouge (1967). [5] K. Geba and A. Granas, Infinite dimensional cohomology theories (to appear). Zbl0248.57003MR418137
  51. [6] A. Granas, The theory of compact vector fields and some of its applications to topology of functional spaces, I. Rozprawy Matematyczne30, Warszawa (1962). Zbl0111.11001MR149253
  52. [7] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press (1941). MR6493JFM67.1092.03
  53. [8] J. Leray, Topologie des espaces de Banach, C.R. Acad. Sci. Paris, 200 (1935), pp. 1082-1084. Zbl0011.16402
  54. [9] J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann.Sci., Ec. Norm. Sup. (3), 51 (1934), pp. 45-78. Zbl60.0322.02MR1509338JFM60.0322.02
  55. [10] L. Pontrjagin, The general topological theorem of duality for closed sets, Ann. of Math.35 (1934) pp. 904-914. Zbl60.0531.01MR1503203JFM60.0531.01
  56. [11] J. Schauder, Invarianz des Gebietes in Funktionalräumen, Studia Math.1 (1929), pp. 123-139. Zbl55.0242.02JFM55.0242.02
  57. [12] E. Spanier, Duality and S-theory, Bull. Amer. Math. Soc.62 (1956), pp. 194-203. Zbl0072.18001MR85506
  58. [13] E. Spanier and J.H.C. Whitehead, Duality in homotopy theory, Mathematika, 2 (1955), pp. 56-80. Zbl0064.17202MR74823
  59. [14] G.W. Whitehead, Generalized homology theories, Trans. Amer. Math. Soc.102 (1962), pp. 227-283. Zbl0124.38302MR137117

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