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, $S(n)$-$\hat{I}¸$-closed, weakly $S(n)$-closed and weakly $S(n)$-$\hat{I}¸$-closed spaces for each $n\in \mathbb{N}$. The relation of these classes in Lindelöf spaces is shown. Some of the solved problems formulated by D. Dikranjan and E. Giuli are presented in the examples.

19 pages, 10 figures, 2 diagrams