Axioms (Apr 2022)
On Soft Generalized <i>ω</i>-Closed Sets and Soft <i>T</i><sub>1/2</sub> Spaces in Soft Topological Spaces
Abstract
In this paper, we define a soft generalized ω-closed set, which is a generalization of both the soft ω-closed set and the soft generalized closed set. We show that the classes of generalized closed sets and generalized ω-closed sets coincide in soft anti-locally countable soft topological spaces. Additionally, in soft locally countable soft topological spaces, we show that every soft set is a soft generalized ω-closed set. Furthermore, we prove that the classes of soft generalized closed sets and soft generalized ω-closed sets coincide in the soft topological space (X,τω,A). In addition to these, we determine the behavior of soft generalized ω-closed sets relative to soft unions, soft intersections, soft subspaces, and generated soft topologies. Furthermore, we investigate soft images and soft inverse images of soft generalized closed sets and soft generalized ω-closed sets under soft continuous, soft closed soft transformations. Finally, we continue the study of soft T1/2 spaces, in which we obtain two characterizations of these soft spaces, and investigate their behavior with respect to soft subspaces, soft transformations, and generated soft topologies.
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