Abstract: The purpose of this research is to extend and study types of topological spaces as Lindelof spaces by using coc-r-open sets. In this study, we study and introduce the concepts of coc-r-open sets. A special intrest types of spaces called coc-r-Lindelof and I-coc-r-Lindelof are studied and obtain some of their basic properties.We introduce new types of functions using coc-r-open sets. Moreover, the relation between Lindelof, I-Lindelof, coc-r-Lindelof and I-coc-r-Lindelof spaces are studied and investigated the topological properties of them using coc-r-open sets.