On \(K\Omega\) and Relative Closure Operators in \((P(X))^{\mathbb{N}}\)

Abstract

In this paper, we introduce the notions of a \(K\Omega\)-closure operator, a relative closure operator, and their components. Further on we investigate the relation among themselves, observe additivity and productivity behavior of the operators and study the sequential topologies (ST) induced by them. Two dimensional expansion, in some sense, of a sequential set by the aforementioned operators plays the main and important role in this paper.