On Soft Generalized ω-Closed Sets and Soft T1/2 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.

Soft C-continuity and soft almost C-continuity between soft topological spaces

“…Soft topological concepts were established by Shabir and Naz to be equivalent to their counterparts in classical topology, which motivated and supported researchers in the field to continue in this direction. Numerous contributions have been made to the exploration of topological notions and concepts in soft environments since the development of soft topology [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] .…”

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.…”

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

“…Soft topology is one of the structures presented as a novel expansion of classical topology by Shabir and Naz [10]. Many classical topological notions have been developed and expanded in soft set contexts (see, [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]), but significant additions remain potential. Thus, the study of soft topology is a current trend among topological researchers.…”

“…We expect that by defining a reasonable new class of soft sets in soft topological spaces, we will pave the way for a lot of future research articles on the subject. Soft ω-open sets, for example, were presented in [26] as a generalization of soft open sets in soft topological spaces, and other related research articles, such as [14,24,25], have appeared. In this paper, we will combine the classes of soft regular open sets and soft ω-closed sets to define soft regular generalized ω-closed sets as a new class of sets that contains the classes of soft regular closed sets and soft regular generalized ω-closed sets.…”

“…In this paper, STS and TS will be used in this study to signify soft topological space and topological space, respectively. We shall use the concepts and terminologies from [14,26,27] throughout this paper. Now, we shall recollect several notions that will be employed in the sequel.…”