A general selection theorem for a Vietoris-like hyperspace topology is obtained and, as a result, several known selection theorems for both `topology'- and `metric'-generated hyperspace topologiesare improved from a common point of view. Applications arepresented in characterizing classes of metrizable spaces bycontinuous selections for their hyperspaces.
1991 Mathematics Subject Classification: primary 54B20, 54C65; secondary 54E45, 54D65, 54E40, 54C10, 54G12.