Continuity of set valued maps

In this work, which consist of four chapters, some properties of converges sequences of sets, Hausdorff and Vietories topologies denned on hyperspaces and Hausdorff and Vietories continuties of set valued maps have been studied. In the first chapter, some important definitions, theorems with proofs and metrics are given. The second chapter deals with Kuratowski and Hausdorff convergences of sequences of sets. The definitions and some properties of this type convergences sequences have been given. The third chapter concerns with Hausdorff and Vietories topologies denned on hyperspaces. Some properties and relationships between these topologies have been investigated. In the last section, Hausdorff and Vietories continuties of set valued maps and various characterizations of these types continuities have been studied. Also, relationship between closednes of graphs of set valued maps and these continuities have been given. As a result, these two continuity types have been compared with each other. Keywords: Set valued maps, Lower-Upper semi continuous.