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

2025/08/13 by Osipov, Alexander V.
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2508.09572

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)-θ-closed, weakly S(n)-closed and weakly S(n)-θ-closed spaces for each n∈ 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.

Citations

• Cardinal inequalities for S(n)-spaces
• On the cardinality of S(n)-spaces
• On cardinality bounds for θⁿ-Urysohn spaces

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