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Resumen:
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An upper semicontinuous multivalued map F:X?Y is said to be ? -small if the diameter of F(x) is less than ? for each x?X . F and G are ? -homotopic if there is an ? -small homotopy H:X×I?Y joining F and G . F:X×[0,?)?Y is a fine multivalued map if for each ?>0 there is m?0 such that F|X×[m,?) is ? -small. Fine multivalued maps F,G:X×[0,?)?Y are homotopic provided for each ?>0 there is m?0 such that F|X×[m,?) is ? -homotopic to G|X×[0,?) . The main result of the paper is to show a bijective correspondence between shape morphisms from X to Y , X and Y being compact metrizable, and homotopy classes of fine multivalued maps from X×[0,?) to Y .
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