On soft sets and topology

In 1999, the soft set theory introduced by Molodtsov to remove various uncertainties quickly attracted attention and was accepted by many researchers as a new mathematical tool. Mathematicians working in this new field have made important contributions to the development of the subject. On the one hand, it is aimed to develop soft theory by using classical theory, while on the other hand the relation of new concepts obtained with classical theory is emphasized. In this thesis, the definitions which constitute the basis of the soft set theory are given and the soft topological spaces are constructed by soft Kuratowski closure and soft interior operators. Then, soft interior, soft cluster, soft exterior, soft boundary definations and derived from them are soft sets defined from, based on different soft point definitions in the literature. Soft topological spaces have been reexamined in the light of these definitions. As a result, it has been obtained some different results familiar from classical set theory and classical topological spaces. In addition, soft metric spaces have been studied and the relationship between soft metric spaces and classical metric spaces has been described. At this point, some metric constructions which are generalizations of classical metric spaces are considered and it is observed that soft metrics actually correspond to conic metric concept which is one of these generalizations. Thus, conclusions have been reached that all fixed point theorems obtained on conic metric spaces can be transferred to soft metric spaces without any additional condition.