%0 Journal Article
%A Rodríguez Sanjurjo, José Manuel
%T Selections of multivalued maps and shape domination
%D 1990
%@ 0305-0041
%U https://hdl.handle.net/20.500.14352/57697
%X 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. Čerin, 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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