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On the uniqueness of the topological degree. (English) Zbl 0249.55004

MSC:
55M25 Degree, winding number
47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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[1] Borisovic, Ju. G.: Rotation of weakly continuous vector fields. Doklady Akad. Nauk. SSSR131, 230-233 (1960) (=Soviet. Math. Doklady1, 214-217 (1960)).
[2] Borisovic, Ju. G., Sopronov, Ju. I.: A contribution to the topological theory of condensing operators. Doklady Akad. Nauk. SSSR183, 18-20 (1968) (=Soviet. Math. Doklady9, 1304-1307 (1968)).
[3] Brouwer, L.E.J.: Über Abbildungen von Mannigfaltigkeiten. Math. Ann.71, 97-115 (1912). · JFM 42.0417.01 · doi:10.1007/BF01456931
[4] Browder, F.E.: On the fixed point index for continuous mappings of locally connected spaces. Summa Brasil. Math.4, 253-293 (1960). · Zbl 0102.37901
[5] Browder, F.E.: Semicontractive and semiaccretive nonlinear mappings in Banach spaces. Bull. Amer. Math. Soc.74, 660-665 (1968). · Zbl 0164.44801 · doi:10.1090/S0002-9904-1968-11983-4
[6] Browder, F.E.: Topology and nonlinear functional equations. Studia Math.31, 189-204 (1968). · Zbl 0176.45303
[7] Browder, F.E., Nussbaum, R.D.: The topological degree for noncompact nonlinear mappings in Banach spaces. Bull. Amer. Math. Soc.74, 671-676 (1968). · Zbl 0164.17002 · doi:10.1090/S0002-9904-1968-11988-3
[8] Browder, F.E., Petryshyn, W.V.: The topological degree and Galerkin approximations for noncompact operators in Banach spaces. Bull. Amer. Math. Soc.74, 641-646 (1968). · Zbl 0164.17003 · doi:10.1090/S0002-9904-1968-11973-1
[9] Browder, F.E., Petryshyn, W.V.: Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces. J. Funct. Anal.3, 217-245 (1968). · Zbl 0177.42702 · doi:10.1016/0022-1236(69)90041-X
[10] Cronin, J.: Fixed points and topological degree in nonlinear analysis. Amer. Math. Soc. Surveys 11, Providence, R.I. 1964. · Zbl 0117.34803
[11] Darbo, G.: Punti uniti in trasformazioni a condominio non compato. Rend. Sem. Mat. Univ. Padova24, 353-367 (1955). · Zbl 0064.35704
[12] Elworthy, K.D.: Fredholm maps andGL C (E) structures. Bull. Amer. Math. Soc.74, 582-586 (1968). · Zbl 0159.25102 · doi:10.1090/S0002-9904-1968-12018-X
[13] Elworthy, K.D., Tromba, A.: Differential structures and Fredholm maps on Banach manifolds. Proc. Sympos. Pure Math. Vol. 18, Amer. Math. Soc., Providence, R.I. 1970. · Zbl 0206.52504
[14] Elworthy, K.D., Tromba, A.: Degree theory on Banach manifolds. Proc. Sympos. Pure Math. Vol. 15, Amer. Math. Soc., Providence R.I. 1970. · Zbl 0234.58002
[15] Fenske, C.: Analytische Theorie des Abbildungsgrades für Abbildungen in Banachräumen. Math. Nachr.48, 279-290 (1971). · Zbl 0212.16501 · doi:10.1002/mana.19710480121
[16] Führer, L.: Theorie des Abbildungsgrades in endlichdimensionalen Räumen. Inaugural-Dissertation, Freie Universität Berlin 1971.
[17] Frum-Ketkoy, R. L.: On mappings of the sphere of a Banach space. Doklady Akad. Nauk. SSSR155, 1229-1231 (1967) (=Soviet. Math. Doklady8, 1004-1009 (1967)).
[18] Heinz, E.: An elementary analytic theory of the degree of a mapping inn-dimensional space. J. Math. Mech.8, 231-247 (1959). · Zbl 0085.17105
[19] Krasnoselskii, M. A.: Topological methods in the theory of nonlinear integral equations. New York: Pergamon Press 1964.
[20] Kuiper, Nicholas H.: The homotopy type of the unitary group of Hilbert space. Topology3, 19-30 (1965). · Zbl 0129.38901 · doi:10.1016/0040-9383(65)90067-4
[21] Leray, J.: Lá théorie des points fixes et ses applicationes en analyse. Proc. Internat. Congr. Math., Vol. 2, Cambridge Mass., 1950, pp. 202-208, Amer. Math. Soc., Providence, R.I. 1952.
[22] Leray, J., Schauder, J.: Topologie et équations fonctionelles. Ann. Sci. Ecole. Norm. Sup,3, 51, 45-78 (1934). · JFM 60.0322.02
[23] Nagumo, M.: A theory of degree of mapping based on infinitesimal analysis. Amer. J. Math.73, 485-496 (1951). · Zbl 0043.17802 · doi:10.2307/2372303
[24] Nagumo, M.: Degree of mappings in locally convex topological vector spaces. Amer. J. Math.73, 497-511 (1951). · Zbl 0043.17801 · doi:10.2307/2372304
[25] Nussbaum, R.D.: The fixed point index for local condensing maps. Ann. Math. Pura Appl.89, 217-258 (1971). · Zbl 0226.47031 · doi:10.1007/BF02414948
[26] Nussbaum, R.D.: Degree theory for local condensing maps. J. Math. Anal. and Appl.37, 741-766 (1972). · Zbl 0232.47062 · doi:10.1016/0022-247X(72)90253-3
[27] O’Neill, B.: Essential sets and fixed points. Amer. J. Math.75, 497-509 (1953). · Zbl 0050.39202 · doi:10.2307/2372499
[28] Rothe, E.: Zur Theorie der topologischen Ordnung und der Vektorfelder in Banachschen Räumen. Compositio Math.5, 177-197 (1937). · Zbl 0018.13304
[29] Rothe, E.: The theory of topological order in some linear topological spaces. Iowa State College J. of Science13, 373-390 (1939), Math. Rev. 1 (1940) p. 108, microfilm=495. · JFM 65.0499.01
[30] Rothe, E.: Mapping degree in Banach spaces and spectral theory. Math. Z.63, 195-218 (1955). · Zbl 0065.35503 · doi:10.1007/BF01187933
[31] Sard, A.: The measures of the critical values of differentiable maps. Bull. Amer. Math. Soc.48, 883-890 (1942). · Zbl 0063.06720 · doi:10.1090/S0002-9904-1942-07811-6
[32] Schaefer, H.: Topological vector spaces. New York: Macmillan 1966. · Zbl 0141.30503
[33] Schauder, J.: Der Fixpunktsatz in Funktionalräumen. Stuida Math.2, 170-179 (1930). · JFM 56.0355.01
[34] Schwartz, J.: Nonlinear functional analysis. New York: Gordon and Breach 1969. · Zbl 0203.14501
[35] Smale, S.: An infinite-dimensional version of Sard’s theorem. Amer. J. Math.87, 861-866 (1965). · Zbl 0143.35301 · doi:10.2307/2373250
[36] Wong, H.S.F.: The topological degree ofA-proper maps. Canadian J. Math.23, 403-412 (1971). · Zbl 0215.21303 · doi:10.4153/CJM-1971-042-5
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