Topics in infinite dimensional topology
Séminaire Jean Leray, no. 3 (1969-1970), pp. 1-131. 
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     author = {Granas, Andrzej},
     title = {Topics in infinite dimensional topology},
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     url = {http://archive.numdam.org/item/SJL_1969-1970___3_1_0/}
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Granas, Andrzej. Topics in infinite dimensional topology. Séminaire Jean Leray, no. 3 (1969-1970), pp. 1-131. http://archive.numdam.org/item/SJL_1969-1970___3_1_0/

[1] R.F. Arens and J. Eells, Jr., On embedding uniform and topological spaces, Pacific J. Math., 6 (1956), 397-403. | MR | Zbl

[2] M. Artin and B. Mazur, On periodic points, Ann. of Math. 81 (1965), 82-99. | MR | Zbl

[3] G.D. Birkhoff and O.D. Kellogg, Invariant points in function spaces, Trans. Amer. Math., Soc. 23 (1922). | JFM | MR

[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. | MR | Zbl

[5] K. Borsuk, Sur un continu acyclique qui se laisse transformer topologiquement en lui-même sans points invariants, Fund. Math., 24 (1934), 51-58. | Zbl

[6] - Theory of retracts, PWN, Warszawa, 1967. | Zbl

[7] C. Bowszyc, Fixed point theorems for the pairs of spaces, BAPS 16 (1968), 845-850. | MR | Zbl

[8] - On the Euler-Poincaré characteristic of a map and the existence of periodic points, Bull. Acad. Polon, Sci. 17 (1969), 367-372. | MR | Zbl

[9] - Some theorems in the Theory of Fixed Points, (Thesis), University of Warsaw (1969) (in polish).

[10] D.G. Bourgin, Un indice dei punti, I, II, Atti. Acad. Naz. Lincei 8, 19 (1955), 435-440, 20 (1956), 43-48. | Zbl

[11] - Fixed points on neighbourhood retracts, Revue Math. Pures Appl. 2, Hommage à S. Stoilow (1957), 371-374. | MR | Zbl

[12] F.E. Browder, On the fixed point index for continuous mappings of locally connected spaces, Summa Bras. Math. 4 (1960), 253-293. | MR | Zbl

[13] - Fixed point theorems on infinite dimensional manifolds, Trans. Am. Math. Soc. 119, 2 (1965), 179-194. | MR | Zbl

[14] A. Deleanu, Théorie des points fixes: sur les rétractes de voisinage des espaces convexoïdes, Bull. Soc. Math. Fr., 87 (1959), 235-243. | Numdam | MR | Zbl

[15] A. Dold, Fixed point index and fixed point theorem for Euclidean neighbourhood retracts, Topology, 4 (1965), 1-8. | MR | Zbl

[16] J. Dugundji, An extension of Tietze's theorem, Pacific Journ. Math. 1 (1951). | MR | Zbl

[17] S. Eilenberg and D. Montgomery, Fixed point theorems for multi-valued transformation, Amer. Journ. of Math. 58 (1946), 214-222. | MR | Zbl

[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. | MR | Zbl

[19] F.B. Fuller, The existence of periodic points, Ann. of Math. 57 (1953), 229-230. | MR | Zbl

[20] A. Gmurczyk, On approximative retracts, Bull. Acad. Polon. Sci. 16 (1968), 9-14. | MR | Zbl

[21] L. Górniewicz and A. Granas, Fixed point theorems for multi-valued mappings of the absolute neighbourhood retracts, (to appear). | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[24] - Generalizing the Hopf-Lefschetz fixed point theorem for non-compact ANR-s, Symposium on Infinite Dimensional Topology, Bâton-Rouge, 1967. | Zbl

[25] - Fixed point theorems for the approximative ANR-s, Bull. Acad. Polon. Sci. 16 (1968), 15-19. | MR | Zbl

[26] - Some theorems in fixed point theory. The Leray-Schauder Index and the Lefschetz Number, Bull. Acad. Polon. Sci. 17 (1969), 131-137. | MR | Zbl

[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. | MR | Zbl

[28] H. Hopf, Eine Verallgemeinerung der Euler-Poincaréschen Formel, Nachr. Ges. Wiss., Göttingen (1928). | JFM

[29] M. Hukuhara, Sur l'application semi-continue dont la valeur est un compact convexe, Funkcialaj Ekvacioj 10 (1967), 43-66. | MR | Zbl

[30] J.W. Jaworowski, Theorems on antipodes for multi-valued mappings and a fixed point theoren, Bull. Acad. Polon. Sci. 4 (1956), 187-192. | MR | Zbl

[31] - Some consequences of the Vietoris Mapping Theorem, Fund. Math. 45 (1958), 261-272. | Zbl

[32] S. Kinoshita, On some contractible continua without fixed point property, Func. Math. 49 (1953), 96-98. | MR | Zbl

[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. | MR | Zbl

[34] - Fixed-point theorems for multi-valued mappings and optimal control problems Bull. Acad. Polon. Sci. 16 (1968), 645-649. | MR | Zbl

[35] S. Lefschetz, Intersections and transformations of complexes and manifolds, Trans. Amer. Math. Soc. 28 (1926), 1-49. | JFM | MR

[36] - On locally-connected and related sets, Annals of Math. 35 (1934), 118-129. | JFM | MR | Zbl

[37) J. Leray, Sur les équations et les transformations, J. Math. Pures Appl. 24 (1945), 201-248. | Numdam | MR | Zbl

[38] - La théorie des points fixes et ses applications en analyse, Proc. Int. Math. Congress, Cambridge 1950, vol. 2, 202-208. | MR | Zbl

[39] - Théorie des points fixes : indice total et nombre de Lefschetz, Bull. Soc. Math. Fr. 87 (1959), 221-233. | Numdam | MR | Zbl

[40] - Fixed point index and Lefschetz number, Proc. Symp. on Infin. Dimen. Topology, Bâton-Rouge (1967). | Zbl

[41] J. Leray et J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup. 51 (1934). | JFM | Numdam | Zbl

[42] M. Nagumo, Degree of mapping in convex linear topological spaces, Am. J. Math. 73 (1951), 497-511. | MR | Zbl

[43] H. Noguchi, A generalization of absolute neighbourhood retracts, Kodai Math. Seminar Reports 1 (1953), 20-22. | MR | Zbl

[44] J. Schauder, Der Fixpunktsaztz in Funktionalräumen, Studia Math. 2 (1930). | JFM

[45] E.H. Spanier, Algebraic Topology, Mc Graw Hill (1966). | MR | Zbl

[46] L. Vietoris, Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann. 97 (1927), pp. 454-472. | JFM | MR

[1] P. Alexandroff, Dimensionstheorie. Ein Beitrag zur Geometrie der abgeschlossenen Mengen, Math. Ann. 106 (1932), pp. 161-238. | JFM | MR

[2] K. Geba, Algebraic topology methods in the theory of compact fields in Banach spaces, Fund. Math. 54 (1964), pp. 177-209. | MR | Zbl

[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. | Zbl

[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). | MR | Zbl

[6] A. Granas, The theory of compact vector fields and some of its applications to topology of functional spaces, I. Rozprawy Matematyczne 30, Warszawa (1962). | MR | Zbl

[7] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press (1941). | JFM | MR

[8] J. Leray, Topologie des espaces de Banach, C.R. Acad. Sci. Paris, 200 (1935), pp. 1082-1084. | Zbl

[9] J. Leray and J. Schauder, Topologie et Équations Fonctionnelles, Ann. Sci., Ec. Norm. Sup. (3), 51 (1934), pp. 45-78. | JFM | Numdam | MR

[10] L. Pontrjagin, The general topological theorem of duality for closed sets, Ann. of Math. 35 (1934) pp. 904-914. | JFM | MR

[11] J. Schauder, Invarianz des Gebietes in Funktionalräumen, Studia Math. 1 (1929), pp. 123-139. | JFM

[12] E. Spanier, Duality and S-theory, Bull. Amer. Math. Soc. 62 (1956), pp. 194-203. | MR | Zbl

[13] E. Spanier and J.H.C. Whitehead, Duality in homotopy theory, Mathematika, 2 (1955), pp. 56-80. | MR | Zbl

[14] G.W. Whitehead, Generalized homology theories, Trans. Amer. Math. Soc. 102 (1962), pp. 227-283. | MR | Zbl