Koporkh K. Topology Vietoris and Wijsman on the space of quotient objects of compact Hausdorff spaces.

The dissertation is devoted to investigation of categorical and topological properties of space of quotient objects of compact Hausdorff space. We propose different topologizations of the set of quotient objects of compact Hausdorff space, like co-finite topology, open-finite topology, open-open topology, Wijsman topology and Vietoris topology. It is shown that partial order and operation of multiplication are continuous on the set of quotient objects of compact Hausdorff space in Wijsman's and Vietori's topology. One of the most important results of the thesis is determination of properties of the space quotient objects for the convergent sequence or the unit segment or the unit circle.