In 1997, Caldas [1] has introduced a new seperation axiom semi-D 1 which is situated between semi-T^ and semi-T^ due to Maheshwari and Prasad [5]. In 1996, Hatır, Noiri and Yüksel [2] defined C-sets and C-continuity in topological spaces to obtain a decomposition of continuity. Quite recently, Jafari [3] has used the C-sets to define and investigate C-T^ spaces, C-compact spaces and C-connected spaces. In this paper, define cD-sets as the difference set of C-sets and use these sets to define C-D -spaces, cD-corapact spaces and cD-connected spaces. We also investigate the relationship between these spaces and C-continuity (or C-irresoluteness).