Resumen:
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Given an approximate mapping f ? ={f k }:X?Y between compacta from the Hilbert cube [K. Borsuk, Fund. Math. 62 (1968), 223–254, the author associates with f ? a (u.s.c.) multivalued mapping F:X?Y . If F is single-valued, F and f ? induce the same shape morphism, S(F)=S(f ? ) . If Y is calm [Z. ?erin, Pacific J. Math. 79 (1978), no. 1, 69–91 and all F(x) , x?X , are sufficiently small sets, then the existence of a selection for F implies that S(f ? ) is generated by some mapping X?Y . If F is associated with f ? and admits a coselection (a mapping g:Y?X such that y?F(g(y)) , for y?Y ), then S(f ? ) is a shape domination and therefore sh(Y)?sh(X) . If Y is even an FANR, then every sufficiently small multivalued mapping F:X?Y , which admits a coselection, induces a shape domination S(F) .
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