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

Alexander V. Osipov

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arXiv · 2508.09572

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

Alexander V. Osipov

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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.

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BibTeX RIS

Alexander V. Osipov. 2025-08-13. Various $S(n)$-closednesses in $S(n)$-spaces with examples. https://arxiv.org/abs/2508.09572

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