STATISTICAL CONVERGENCE IN TOPOLOGICAL SPACE CONTROLLED BY MODULUS FUNCTION

Abstract

The notion of $f$-statistical convergence in topological space, which is actually a statistical convergence's generalization under the influence of unbounded modulus function is presented and explored in this paper. This provides as an intermediate between statistical and typical convergence. We also present many counterexamples to highlight the distinctions among several related topological features. Lastly, this paper is concerned with the notions of $s^{f}$-limit point and $s^{f}$-cluster point for a unbounded modulus function $f$