Voytsitskyy R. Extension and topological properties of hyperspaces.

The thesis is devoted to investigating extensional and topological properties of hyperspaces. We characterize metric spaces whose hyperspaces endowed with the Hausdorff metric topology and Attouch-Wets topology are absolute neighborhood extensors. The topological structure of hyperspaces with the Hausdorff metric topology, Attouch-Wets topology and Fell topology is described. In investigating of extensional and topological properties of hyperspaces an approach is developed which is based on the Lawson semilattices theory. The cardinal characteristics of hyperspaces with the Fell topology are founded.