Introduction to elementary soft topological spaces

In this thesis, new topological structures are constructed on soft sets. First, a topology in the classical sense is constructed on classes of soft elements, and then a new soft topology is defined on the soft sets using elementary operations. This new topology is called elementary soft topology. The elementary soft topology has been proven to be related to the soft topologies found in the literature and the topology constructed on the classes of soft elements, and has been demonstrated to be different from other soft topologies. Thus, in the elementary soft topological spaces, important topological concepts such as soft open and soft closed set, soft neighborhood, soft interior element, soft closure element, soft base and soft local base are defined and many features of them are proved. In addition to this, by introducing concepts of soft mapping and soft function on the classes of soft elements, soft continuous functions on elementary soft topological spaces and some properties of them are investigated. Finally, elementary soft product and elementary soft quotient space are studied.