×

The Leray-Schauder index and the fixed point theory for arbitrary ANRs. (English) Zbl 0236.55004


MSC:

55M20 Fixed points and coincidences in algebraic topology
55M25 Degree, winding number
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML

References:

[1] ARENS (R. F.) and EELLS (J., Jr) . - On embedding uniform and topological spaces , Pacific J. Math., t. 6, 1956 , p. 397-403. Article | MR 18,406e | Zbl 0073.39601 · Zbl 0073.39601
[2] BIRKHOFF (G. D.) and KELLOGG (O. D.) . - Invariant points in function spaces , Trans. Amer. math. Soc., t. 23, 1922 , p. 96-115. MR 1501192 | JFM 48.0472.02 · JFM 48.0472.02
[3] BORSUK (K.) . - Theory of retracts . - Warszawa, PWN - Polish scientific Publishers, 1967 (Polska Akad. Nauk, Monographie matem., 44). MR 35 #7306 | Zbl 0153.52905 · Zbl 0153.52905
[4] BOURGIN (D. G.) . - Un indice dei punti, I, II , Atti Acad. naz. dei Lincei, Série 8, t. 19, 1955 , p. 435-440 ; t. 20, 1956 , p. 43-48. MR 17,1120g | Zbl 0073.39706 · Zbl 0073.39706
[5] BROWDER (F. E.) . - On the fixed point index for continuous mappings of locally connected spaces , Summa bras. Math., t. 4, 1960 , p. 253-293. MR 26 #4354 | Zbl 0102.37901 · Zbl 0102.37901
[6] BROWDER (F. E.) . - Fixed point theorems on infinite dimensional manifolds , Trans. Amer. math. Soc., t. 119, 1965 , p. 179-194. MR 33 #3287 | Zbl 0132.18803 · Zbl 0132.18803
[7] DELEANU (A.) . - Théorie des points fixes sur les rétractes de voisinages des espaces convexoïdes , Bull. Soc. math. France, t. 87, 1959 , p. 235-243. Numdam | MR 26 #763 | Zbl 0093.36801 · Zbl 0093.36801
[8] DOLD (A.) . - Fixed point index and fixed point theorem for euclidean neigh-bourhood retracts , Topology, Oxford, t. 4, 1965 , p. 1-8. MR 33 #1850 | Zbl 0135.23101 · Zbl 0135.23101
[9] DUGUNDJI (J.) . - An extension of Tietze’s theorem , Pacific J. Math., t. 1, 1951 , p. 353-367. Article | MR 13,373c | Zbl 0043.38105 · Zbl 0043.38105
[10] GRANAS (A.) . - The theory of compact vector fields and some of its applications to topology of functional spaces , Rozprawy Matematyczne, Warszawa, n^\circ 30, 1962 , 93 pages. MR 26 #6743 | Zbl 0111.11001 · Zbl 0111.11001
[11] GRANAS (A.) . - Generalizing the Hopf-Lefschetz fixed point theorem for non-compact ANR-s , Symposium on infinite dimensional topology [ 1967 . Bâton Rouge]. Zbl 0235.55008 · Zbl 0235.55008
[12] GRANAS (A.) . - Some theorems in fixed point theory. The Leray-Schauder index and the Lefschetz number , Bull. Acad. polon. Sc., t. 17, 1969 , p. 131-137. MR 39 #7588 | Zbl 0185.51204 · Zbl 0185.51204
[13] GRANAS (A.) . - Topics in infinite dimensional topology , Séminaire Leray, 9e année, 1969 - 1970 , fasc. 3. Numdam · Zbl 0185.51204
[14] KNILL (R.) . - On the homology of a fixed point set , Bull. Amer. math. Soc., t. 77, 1971 , p. 184-190. Article | MR 45 #9320 | Zbl 0214.49902 · Zbl 0214.49902
[15] LERAY (J.) . - Sur les équations et les transformations , J. Math. pures et appl. 9e série, t. 24, 1945 , p. 201-248. MR 7,468g | Zbl 0060.40705 · Zbl 0060.40705
[16] LERAY (J.) . - Théorie des points fixes : indice total et nombre de Lefschetz , Bull. Soc. math. France, t. 87, 1959 , p. 221-233. Numdam | MR 26 #762 | Zbl 0093.36702 · Zbl 0093.36702
[17] LERAY (J.) . - Fixed point index and Lefschetz number , Symposium on infinite dimensional topology [ 1967 . Bâton Rouge]. Zbl 0235.55007 · Zbl 0235.55007
[18] LERAY (J.) et SCHAUDER (J.) . - Topologie et équations fonctionnelles , Ann. scient. Éc. Norm. Sup., t. 51, 1934 , p. 45-78. Numdam | Zbl 0009.07301 | JFM 60.0322.02 · Zbl 0009.07301
[19] NAGUMO (M.) . - Degree of mapping in convex linear topological spaces , Amer. J. Math., t. 73, 1951 , p. 497-511. MR 13,150b | Zbl 0043.17801 · Zbl 0043.17801
[20] SCHAUDER (J.) , - Der Fixpunktsatz in Funktionalraumen , Studia Math., Warszawa, t. 2, 1930 , p. 171-196. Article | JFM 56.0355.01 · JFM 56.0355.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.