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Sur la méthode de l’homotopie dans la théorie des points fixes pour les applications multivoques. II: L’indice dans les ANR-s compacts. (On the homotopy method in the fixed point theory for set-valued maps. II: The index in compact ANR-s). (French) Zbl 0678.54033
Summary: We announce here several fixed point results for set-valued maps; these are obtained by combining the homotopy method [K. Geba, A. Granas, T. Kaczyński and W. Krawcewicz, C. R. Acad. Sci., Paris, Sér. I 300, 303-306 (1985; Zbl 0585.47049)] and the approximation techniques initiated by A. Cellina and A. Lasota [Atti Acad. Naz. Lincei, Rend., Cl. Sci. Fis. Mat. Natur., VIII Ser. 47, 434-440 (1969; Zbl 0194.448)]. We establish, in particular, in a simple way the fixed point index theory for u.s.c. set-valued maps with $$R_{\delta}$$ values in the compact ANR-s.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) 55M20 Fixed points and coincidences in algebraic topology