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In this talk, we defined the notion of I^K-closed (resp. I^K-open) set in a T.S. (X, T ) and established some important results concerning this notion. Furthermore, we defined the I^K-Sequential topological space which is a generalized form of the I^∗-sequential space. We also talked about I^K-continuity of functions and saw that in I^K-Sequential topological space, the notion of continuity and sequential continuity are the same. In the last section of the paper, the subspace of I^K-sequential space has been studied and some important results established.