-convex sets and -convex functions, which are considered as an important class of generalized convex sets and convex functions, have been introduced and studied by Youness [5] and other researchers. This class has recently extended, by Youness, to strongly -convex sets and strongly -convex functions. In these generalized classes, the definitions of the classical convex sets and convex functions are relaxed and introduced with respect to a mapping . In this paper, new properties of strongly -convex sets are presented. We define strongly -convex hull, strongly -convex cone, and strongly -convex cone hull and we proof some of their properties.  Some examples to illustrate the aforementioned concepts and to cl

In this paper, we offer and study a novel type generalized soft-open sets in topological spaces, named soft Æ„c-open sets. Relationships of this set with other types of generalized soft-open sets are discussed, definitions of soft Æ„ , soft bc- closure and soft bc- interior are introduced, and its properties are investigated. Also, we introduce and explore several characterizations and properties of this type of sets.

    In this paper, the concept of soft closed groups is presented using the soft ideal pre-generalized open and soft pre-open, which are -ᶅ- - -closed sets " -closed", Which illustrating several characteristics of these groups.  We also use some games and   -  Separation Axiom, such as (Æ®_0, Ó¼, ᶅ) that use many tables and charts to illustrate this. Also, we put some proposals to study the relationship between these games and give some examples.

In this paper we define a signal soft set as a mathematical tool to represent and study atoms, anti-atoms, electrons, anti-electrons, protons, and anti-protons, and generate a signal soft topology, with an example of signal soft topology on H₂O.

The concept of strong soft  pre-open set was initiated by Biswas and Parsanann.We utilize this notion to study several characterizations and properties of this set. We investigate the relationships between this set and other types of soft open sets. Moreover, the properties of the strong soft  pre-interior and closure are discussed. Furthermore, we define a new concept by using strong soft  pre-closed that we denote as locally strong soft  pre-closed, in which several results are obtained. We establish a new type of soft pre-open set, namely soft  pre-open. Also, we continue to study pre-  soft open set and discuss the relationships among all these sets. Some counter examples are given to show some relations

In this paper, we introduce and study new types of soft open sets and soft closed
sets in soft bitopological spaces (X,~ ,~ ,E) 1 2   , namely, (1,2)*-maximal soft open
sets, (1,2)*-maximal soft (1,2)*-pre-open sets, semi (1,2)*-maximal soft (1,2)*-preopen
sets, (1,2)*-maximal soft closed sets, (1,2)*-maximal soft (1,2)*-pre-closed
sets, (1,2)*-minimal soft open sets, (1,2)*-minimal soft (1,2)*-pre-open sets, (1,2)*-
minimal soft closed sets, (1,2)*-minimal soft (1,2)*-pre-closed sets, and semi (1,2)*-
minimal soft (1,2)*-pre-closed sets. Also, properties and the relation among these
concepts have been studied.

 In this paper, we introduce  and  study  new  classes of soft  open  sets  in soft bitopological spaces called soft  (1,2)*-omega  open  sets  and  weak forms of soft (1,2)*-omega open sets such as soft  (1,2)*-α-ω-open sets, soft  (1,2)*-pre-ω-opensets, soft  (1,2)*-b-ω-open sets,  and  soft  (1,2)*-β-ω-open  sets. Moreover; some basic properties and the relation among these concepts and other concepts also have been studied.