The purpose of this paper is to introduce the notion of soft ideal in soft set theory. The concept of soft local function is also introduced. These concepts are discussed with a view to find new soft topologies from the original one. The basic structure, especially a basis for such generated soft topologies also studied here. Finally, the notion of compatibility of soft ideals with soft topologies is introduced and some equivalent conditions concerning this topic are established here.

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Soft Ideal Theory Soft Local Function and Generated Soft Topological Spaces

In this paper we introduce the notion of supra soft topological spaces. We extend the notion of  -operation, pre-open soft sets,  -open soft sets, semi-open soft sets and  -open soft sets to such spaces and study their properties and the relations between them. Also, we introduce the concepts of supra pre (resp.  - , semi-,  -) continuous soft functions on these spaces and study some of their properties. We show that a mapping between two soft topological spaces is supra  -continuous soft if and only if it is supra pre-continuous soft and supra semi -continuous soft. The importance of this approach is that, the class of supra soft topological spaces is wider and more general than the class of soft topological spaces.

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Decompositions of Some Types of Supra Soft Sets and Soft Continuity

On soft topological ordered spaces

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.

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On Two Classes of Soft Sets in Soft Topological Spaces

In the present paper, we have continued to study the properties of soft top logical spaces. We introduce new types of soft compactness based on the soft ideal Ĩ, in a soft topological space (X ,τ,E) namely, softĨ-compactness, soft semiĨ-compactness, soft countably-̃ I-compactness and soft countably semiĨ-compactness. Also, several of their topological properties are inves t gated. The behaviour of these concepts under various types of soft functions ha s obt ined.

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Soft Semi Compactness via Soft Ideals

In this paper the authors introduce the notions of - operation, pre-open soft sets, -open soft sets, semi-open soft sets and -open soft sets to soft topological spaces. The authors study the relations between these dierent types of subsets of soft topological spaces. The au- thors also introduce the concepts of pre-soft continuous functions, -soft continuous functions, semi-soft continuous functions and -soft continuous functions. Finally, the authors show that a mapping between two soft topo- logical spaces is -soft continuous if and only if it is pre-soft continuous and semi soft continuous. 2010 AMS Classication: 06D72, 54A40

operation and decompositions of some forms of soft continuity in soft topological spaces

The concept of soft ideal was first introduced by Kandil et al. [ 13]. In 1999, Molodtsov [ 22] introduced the concept of soft sets as a general mathematical tool for dealing with uncertain objects. The conc pt of generalized closed soft sets in soft topological spaces was introduced by Kannan [ 15] in 2012. The notions of supra soft topological space were first introd uce by Kandil et al. [ 14]. In this paper, we introduce the concept of supra generalized closed so ft sets(supra g-closed soft for short) in a supra topological space (X ,μ ,E) and study their properties in detail. Also, we introduce the concept of supr a generalized closed soft sets with respect to a soft ideal (supra-̃ Ig-closed soft for short) in a supra topological space (X ,μ ,E) and study their properties in detail, which is the extension of the concept of supra generalized closed soft sets.

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Supra Generalized Closed Soft Sets with Respect to an Soft Ideal in Supra Soft Topological Spaces

The purpose of this paper is to construct a new approach of proximity and generalized proximity based on the soft set. Some results on these spaces have obtained and three of the important results are: every soft T4− space is compatible with a proximity relation on P(X) E. In addition, every soft space is compatible with a Pervin proximity relation on P(X) E. It is also shown that every soft Ro−space is compatible with a Lodato proximity relation on P(X) E.

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O. A. E. Tantawy

Papers

Soft Ideal Theory Soft Local Function and Generated Soft Topological Spaces

operation and decompositions of some forms of soft continuity in soft topological spaces

Soft Semi Compactness via Soft Ideals

Supra Generalized Closed Soft Sets with Respect to an Soft Ideal in Supra Soft Topological Spaces

New Structures of Proximity Spaces