New forms of continuity (δ-α-continuous and contra δ-α-continuous)

Abstract

In this paper‚ we explore the aspects of new forms of continuity‚ by utilizing generalized open sets which play a significant role in General Topology and Real Analysis. Firstly‚ we start this paper by recalling the history and the developments of this subject‚ as well as we include the introduction of topology and the basic concepts in the topology, It defines types of open sets and continuity. In the second section of this paper we introduced and investigated a relatively new notion of open sets; namely ـαـopen sets. Additionally, the comparison of this new notion with αـopen sets have been done. Finally, we apply the notion of δ-α-open sets in topological space to present and study a new classes of functions called δ-α-continuous and contra δ-α-continuousas a new generalization of contra continuity, These functions were compared with αcontinuous and contra α-continuous.