ON $\boldsymbol{\mathcal{I}^\mathcal{K}}$-CONVERGENCE IN TOPOLOGICAL SPACES VIA SEMI-OPEN SETS

A sequence {xn} is S-I K -convergent to , if there exists a 'big enough' subsequence {xn k } which K-converges to via semi-open sets.In this paper, we introduce the concept of S-I K -convergence which generalizes S-I-convergence and discuss some properties, as well as its relation with compact sets.For two given ideals I and K, we justify the existence of an ideal such that I K -convergence and convergence with the third ideal coincides for semi-open sets.Moreover, the notion of S-I K -cluster point of a sequence is defined and studied here.We characterize the collection of S-I K -cluster points of a sequence as semi-closed subsets of the space.