On Soft Topological Spaces

Abstract

Abstract:The classical mathematical theories have their difficulties which are pointed out in [18] for the solution complicated problems in engineering and environment. To overcome these difficulties, Molodtsov [18] introduced the concept of soft set as a new mathematical tool. Furthermore, D. Pei and D. Miao [22] showed that soft sets are a class of special information systems. In [9] for the soft set theory: new definitions, examples, new classes of soft sets, and properties for mappings between different classes of soft sets are introduced and studied. Moreover, the theory of soft topological spaces is investigated. This paper continues the study of the theory of soft topological spaces and presents for this theory new definitions, characterizations, and results concerning separation axioms, convergence, Cartesian product, soft θ -topology, and soft θ -continuity.

On Weakly Soft Omega Open Functions and Weakly Soft Omega Closed Functions in Soft Topological Spaces

“…58, No.2C, pp: 1094-1106 and Ozkan [3], Arockiarani and Arokia Lancy [4], Yuksel and et al [5], and Georgiou and Megaritis [6] defined and study soft α-open sets, soft pre-open sets, soft regular open sets, soft Ө-interior points and soft Ө-cluster points in soft topological spaces respectively. Also, soft open functions and soft closed functions were first introduced by Nazmul and Samanta [7].…”

Soft topological space and topology on the Cartesian product

“…By [9], [10], [21] a soft topological space is a triplet (E, U, τ ), where τ ⊂ SS(E, U ) is a topology. So, τ is represented by a family of set valued mappings F from F(E, U ) each of them has a binary relation representation R F from R(E, U ).…”

“…There has been a rapid growth of interest in soft set theory, its applications and its connection with another mathematical branches [1], [2], [4], [5], [7], [8], [12], [13], [14], [15], [16], [23]. Moreover, there are many papers devoted to soft topological spaces [3], [6], [9] , [10], [11], [17], [21], [22]. The basic topological notions such as the soft open and soft closed sets, soft subspace, soft closure and soft interior, soft boundary, soft separation axioms, soft continuity have been introduced and the investigation of their basic properties has been established.…”

Fuzzy parametrized fuzzy soft topology

“…[6,7,19,27,33]), group theory, ring theory (e.g. [1,2,14,17,21]), and also decision making problems (e.g.…”