Soft Regular Generalized ω-Closed Sets and Soft ω-T1/2 Spaces

Abstract

Soft rgω-closed sets are introduced as a new class of soft sets that strictly contain the classes of soft rg-closed sets and soft gω-closed sets. Furthermore, the behavior of soft rgω-closed sets with respect to soft unions, soft intersections, and soft subspaces, as well as induced soft topologies are investigated. Moreover, soft ω-T1/2 spaces which is a weaker form soft T1/2 spaces is defined and investigated. In addition to these, the characterizations of soft rg-T1/2 spaces and soft rgω-T1/2 spaces are discussed. The work also looks at the relationship between our novel notions in soft topological spaces and their analogs in topological spaces.

Congruence Representations via Soft Ideals in Soft Topological Spaces

“…The work of Ça gman et al [12] and Shabir and Naz [13] had a significant impact on the development of soft topology. Then, many traditional topological notions have been generalized and applied to soft set contexts, such as soft compact spaces [14], soft paracompact spaces [15], soft extremally disconnected spaces [16], soft separation axioms [13,[17][18][19], soft separable spaces [17], and soft connected spaces [15].…”

The soft topology of soft ω ∗ -open sets and soft almost Lindelofness

“…We hope that by establishing a sound new class of soft sets in soft topological spaces, we will open the door to several articles on the topic in the future. Soft ω-open sets, for example, were introduced as a generalization of soft open sets in soft topological spaces in [7], and other research papers on the topic, such as [1][2][3][4][5], have also been published.…”