Some problems on selections for hyperspace topologies

[EN] The theory of hyperspaces has attracted the attention of many mathematicians who have found a large variety of its applications during the last decades. The theory has taken also its natural course and has yielded lots of problems which, besides their independent inner beauty, provide ties with numerous classical fields of mathematics. In the present note we are concerned with some open problems about selections for hyperspace topologies which have been in the scope of our recent research interests.