Selection theorems and minimal mappings in a cluster setting
The domain space of the considered multifunctions is -- besides a topology -- endowed with a sort of path system \({\mathcal E}\) called here a cluster system. Using this additional structure \({\mathcal E}\) the notions of lower and upper \({\mathcal E}\)-continuity, \({\mathcal E}\)-cluster set, \({\mathcal E}\)-closedness of graph, are introduced and investigated. By using those concepts a unified treatment of closed graph theorems, continuous and quasicontinuous selectors and multiselectors and minimality of multifunctions is developed.
scientific article; zbMATH DE number 5934873
scientific article