Set valued topologies

In our thesis we focused on 6 set topologies. These are Hausdorff, Vietoris, Wijsman, Mosco, Fell and Attouch-Wets topologies.The definition and properties of Hausdorff distance are given.Later Hausdorff distance metrik conditions specified. Vietoris topology, which accepts families formed by subsets of open sets and families formed by intersecting open sets, was examined.The Wijsman topology is the topological characterization of a mode of convergence of sets, which is useful in applications and also is a tool in comparing other set convergences. We are referring to the convergence concept which corresponds to the pointwise convergence of the distance functions.Fell topology more rought than Vietoris topology examined and Fell Topology to Kuratowski convergence is compared.Generally given a less restrictive convergence than Kuratowski convergence. This led us to Mosco Topology, which can be used even when $ X $ space is infinite.Last Attouch-Wets topology uniformly bounded sequence of sets, Mosco convergence does not reduce to Hausdorff convergence. Finally, the relationship between these 6 hyperspace topologies is shown.