Various $S(n)$-closednesses in $S(n)$-spaces with examples

Abstract

In this paper we continue to study various types of closures in $S(n)$-spaces. The main results are related to the construction and illustration of examples that allow us to understand the relationship between $S(n)$-closed, $S(n)$-$\theta$-closed, weakly $S(n)$-closed and weakly $S(n)$-$\theta$-closed spaces for each $n\in \mathbb{N}$. The relation of these classes in Lindel\"{o}f spaces is shown. Some of the solved problems formulated by D. Dikranjan and E. Giuli are presented in the examples.