On some properties of IKₛₙ-topological spaces

In this paper, we introduce the notion of I^K_sn-open set and show that the family of I^K_sn-open sets in a topological space forms a topology. The category of I^K-neighborhood spaces is introduced and several properties are obtained there after. Moreover, we obtain a necessary and sufficient condition for the coincidence of the notions ``preserving I^K-convergence'' and `` I^K-continuity'' for any mapping defined on X. Several mappings that are defined on a topological space are shown to be coincident in an I^K-sequential space. The entire investigation is performed in the setting of I^K-convergence which further extends the recentdevelopments [11,13,1].