On soft partial metric spaces

The aim of this thesis is to construct a soft partial metric structure on the soft sets by using soft elements and to examine some topological and completeness properties of the soft partial metric spaces. For this purpose, the following studies has been performed. 1.The soft partial metric space has been defined by the soft element and some examples have been given. 2.The relationships between the soft partial metric space and the soft metric space and the classic partial metric space have been proved. 3.The definitions of the soft ball, soft neighborhood and soft open set in the soft partial metric space have been given and the many properties of their have been proved. It was shown that the elementary union of the soft open sets is a soft open set and under some conditions ((EP5) contition), the elemantary intersection of two soft open sets is a soft open set. It has thus been proved that every soft partial metric space satisfying the condition (EP5) is a soft topological space under elementary operations. 4.The soft closed sets, soft internal sets and soft closure sets in the soft topological partial metric space have been defined and their basic properties have been proved. 5.The definitions of continuous function, homeomorphism and isometry between the soft partial metric spaces have been given and their basic properties have been proved. 6.The convergent and Cauchy sequences of soft elements in soft partial metric space have been examined and the completeness of soft metric space has been studied. Keywords: Soft set, soft element, elementary operations, soft partial metric, topologi of soft partial metric sapaces, converges, completeness.