Soft Semi ω-Open Sets

In this paper, we introduce the class of soft semi ω-open sets of a soft topological space (X,τ,A), using soft ω-open sets. We show that the class of soft semi ω-open sets contains both the soft topology τω and the class of soft semi-open sets. Additionally, we define soft semi ω-closed sets as the class of soft complements of soft semi ω-open sets. We present here a study of the properties of soft semi ω-open sets, especially in (X,τ,A) and (X,τω,A). In particular, we prove that the class of soft semi ω-open sets is closed under arbitrary soft union but not closed under finite soft intersections; we also study the correspondence between the soft topology of soft semi ω-open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi ω-interior and soft semi ω-closure operators via soft semi ω-open and soft semi ω-closed sets. We prove several equations regarding these two new soft operators. In particular, we prove that these operators can be calculated using other usual soft operators in both of (X,τ,A) and (X,τω,A), and some equations focus on soft anti-locally countable soft topological spaces.

Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces

We define soft ωp-openness as a strong form of soft pre-openness. We prove that the class of soft ωp-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ωp-open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ω-open sets are soft ωp-open sets. In addition, we give a decomposition of soft ωp-open sets in terms of soft open sets and soft ω-dense sets. Moreover, we study the correspondence between the soft topology soft ωp-open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft ωp-continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft ωp-continuity. Finally, we study several relationships related to soft ωp-continuity.

Weaker Forms of Soft Regular and Soft T2 Soft Topological Spaces

Soft ω-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ω-regularity as a weaker form of both soft regularity and soft ω-local indiscreetness is defined and investigated. Additionally, soft ω-T2 as a new soft topological property that lies strictly between soft T2 and soft T1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ω-locally indiscreetness (resp. soft ω-regularity) and soft locally indiscreetness (resp. soft ω-regularity). Additionally, it is proved that the induced topological spaces of a soft ω-locally indiscrete (resp. soft ω-regular, soft ω-T2) soft topological space are (resp. ω-regular, ω-T2) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ω-locally indiscrete (resp. ω-regular, ω-T2) topological spaces is soft ω-locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ω-regular and soft ω-T2 soft topological spaces are obtained. Moreover, it is proved that soft ω-regular and soft ω-T2 are hereditarily under soft subspaces.

Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

Connectedness and Local Connectedness on Infra Soft Topological Spaces

This year, we introduced the concept of infra soft topology as a new generalization of soft topology. To complete our analysis of this space, we devote this paper to presenting the concepts of infra soft connected and infra soft locally connected spaces. We provide some descriptions for infra soft connectedness and elucidate that there is no relationship between an infra soft topological space and its parametric infra topological spaces with respect to the property of infra soft connectedness. We discuss the behaviors of infra soft connected and infra soft locally connected spaces under infra soft homeomorphism maps and a finite product of soft spaces. We complete this manuscript by defining a component of a soft point and establishing its main properties. We determine the conditions under which the number of components is finite or countable, and we discuss under what conditions the infra soft connected subsets are components.

New Soft Structure: Infra Soft Topological Spaces

It is always convenient to find the weakest conditions that preserve some topologically inspired properties. To this end, we introduce the concept of an infra soft topology which is a collection of subsets that extend the concept of soft topology by dispensing with the postulate that the collection is closed under arbitrary unions. We study the basic concepts of infra soft topological spaces such as infra soft open and infra soft closed sets, infra soft interior and infra soft closure operators, and infra soft limit and infra soft boundary points of a soft set. We reveal the main properties of these concepts with the help of some elucidative examples. Then, we present some methods to generate infra soft topologies such as infra soft neighbourhood systems, basis of infra soft topology, and infra soft relative topology. We also investigate how we initiate an infra soft topology from crisp infra topologies. In the end, we explore the concept of continuity between infra soft topological spaces and determine the conditions under which the continuity is preserved between infra soft topological space and its parametric infra topological spaces.

INTUITIONISTIC FUZZY SOFT CONTRA GENERALIZED b-CONTINUOUS FUNCTIONS

The main focus of this paper is to introduce the concept of fuzzy soft contra generalized b-continuous functions and fuzzy soft almost generalized b-continuous functions in fuzzy soft topological space. We further studied and established the properties of fuzzy soft contra - continuous functions and fuzzy soft almost generalized b-continuous functions in fuzzy soft topological space.

The Net in a Fuzzy Soft Topological Space and Its Applications

In this paper, the fuzzy soft net is explored to study the properties of a fuzzy soft topological space. Some important results about the closure, separation, and compactness are obtained. It is demonstrated that the net is a powerful tool for studying fuzzy soft topological spaces.

Compactness on Soft Topological Ordered Spaces and Its Application on the Information System

It is well known every soft topological space induced from soft information system is soft compact. In this study, we integrate between soft compactness and partially ordered set to introduce new types of soft compactness on the finite spaces and investigate their application on the information system. First, we initiate a notion of monotonic soft sets and establish its main properties. Second, we introduce the concepts of monotonic soft compact and ordered soft compact spaces and show the relationships between them with the help of examples. We give a complete description for each one of them by making use of the finite intersection property. Also, we study some properties associated with some soft ordered spaces and finite product spaces. Furthermore, we investigate the conditions under which these concepts are preserved between the soft topological ordered space and its parametric topological ordered spaces. In the end, we provide an algorithm for expecting the missing values of objects on the information system depending on the concept of ordered soft compact spaces.

Bipolar neutrosophic soft generalized pre-continuous mappings

In this study, new classes of continuous mappings in bipolar neutrosophic soft topological space, namely bipolar neutrosophic soft continuous mappings and bipolar neutrosophic soft generalized pre-continuous mappings has been introduced. Continuity mappings preserves topological structures such as closeness, openness, compactness and so on. Here, we have proposed and investigated various continuous mappings based on bipolar neutrosophic soft sets. Further, we investigated some of their properties and relations with other mappings with examples.