In this paper, we define soft ω -open sets and strongly soft ω -open sets as two new classes of soft sets. We study the natural properties of these types of soft sets and we study the validity of the exact versions of some known results in ordinary topological spaces regarding ω -open sets in soft topological spaces. Also, we study the relationships between the ω -open sets of a given indexed family of topological spaces and the soft ω -open sets (resp. strongly soft ω -open sets) of their generated soft topological space. These relationships form a biconditional logical connective which is a symmetry. As an application of strongly soft ω -open sets, we characterize soft Lindelof (resp. soft weakly Lindelof) soft topological spaces.

/pdf/on-two-classes-of-soft-sets-in-soft-topological-spaces-4c6vhg4l70.pdf

On Two Classes of Soft Sets in Soft Topological Spaces

In this article, we introduce bipolar hypersoft topological spaces over the collection of bipolar hypersoft sets. It is proven that a bipolar hypersoft topological space gives a parametrized family of hypersoft topological spaces, but the converse does not hold in general, and this is shown with the help of an example. Furthermore, we give a condition on a given parametrized family of hypersoft topologies, which assure that there is a bipolar hypersoft topology whose induced family of hypersoft topologies is the given family. The notions of bipolar hypersoft neighborhood, bipolar hypersoft subspace, and bipolar hypersoft limit points are introduced. Finally, we define bipolar hypersoft interior, bipolar hypersoft closure, bipolar hypersoft exterior, and bipolar hypersoft boundary, and the relations between them, differing from the relations on hypersoft topology, are investigated.

/pdf/topological-structures-via-bipolar-hypersoft-sets-1g2odhcg.pdf

Topological Structures via Bipolar Hypersoft Sets

Pairwise soft separation axioms in soft bitopological spaces

In this paper, we introduce (1, 2)∗-fuzzy soft b-open sets and (1, 2)∗-fuzzy soft b-closed sets in fuzzy soft bitopological space and exhibit the properties of (1, 2)∗-fuzzy soft bopen sets. Then we discuss the relation with (1, 2)∗-fuzzy soft regularopen, (1, 2)∗-fuzzy soft pre-open, (1, 2)∗-fuzzy soft semi-open, (1, 2)∗-fuzzy soft α-open, and (1, 2)∗-fuzzy soft β-open in fuzzy soft bitopological space. Also, we introduce and investigate the concepts of (1, 2)∗-fuzzy soft b-interior, (1, 2)∗-fuzzy soft b-closure in fuzzy soft bitopological space and analyze the relations between these concepts.

/pdf/on-fuzzy-soft-b-open-sets-in-fuzzy-soft-bitopological-space-4p7pv03ex2.pdf

On fuzzy soft b-open sets in fuzzy soft bitopological space

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft  axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is (  space if each coordinate space is soft  space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

Some types of pairwise soft sets and the associated soft topologies

In this paper, we introduce the notion of -separated soft sets based on the soft space ) , , ( 12 E X  which generate by soft bitopological space ) , , , ( 2 1 E X   and study some of its properties. Based on this notion we introduce the notions of -soft connected(disconnected) spaces and study some of their characterizations and properties. Also, we study the connected of -soft sets by using the soft space ) , , ( 12 E X  . Some examples have given to support these concepts.

/pdf/pairwise-soft-connected-in-soft-bitopological-spaces-mt0fxlaxci.pdf

Pairwise Soft Connected in Soft Bitopological Spaces

Kandil and his colleagues [10], introduced the notion of -closed soft set by involving -soft set and -closed soft set. In this paper, we give some additional properties of -closed soft sets. We also introduce and study a related new class of -spaces which lies between  and  . Moreover, we show that there exists a very important relation between the notion of -closed soft sets and the  property, ,  , . In addition, we offer the notion of -locally closed soft sets and we investigate a related new pairwise soft separation axiom  which is independent from . The relationships between the -closed soft sets and the -locally closed soft sets are obtained. Furthermore, we introduce the notion of -open soft sets and we construct supra soft topology associated with the class of -open soft sets and we present pairwise soft separation axioms related to such soft sets, namely . We provide some illustrative examples to support the results.

Shawqi A. Hazza

Papers

Some types of pairwise soft sets and the associated soft topologies

Pairwise soft separation axioms in soft bitopological spaces

Pairwise Soft Connected in Soft Bitopological Spaces

On Pairwise λ-Open Soft Sets and Pairwise Locally Closed Soft Sets