On countability properties of the C-compact-open topology

In this thesis study, which consists of six main chapters, the topological properties of C-compact-open topological space are examined. In the first chapter, the historical process of the thesis topic is given. In the second chapter, definitions and theorems used throughout the thesis are given. In the third chapter, C-compact-open topology is first introduced and some of its features are given. Then, a comparison of C-compact-open topology with other set-open topologies is given. In the last part of the third section, the metrizability features of the C-compact-open topology are discussed. In the fourth chapter, the countability properties of C-compact-open topology are given. In the fifth chapter, the results obtained from the study are briefly summa rized and suggestions for new studies are given. In the sixth chapter, which is the last part of the study, the sources used throughout the thesis are listed.