Countability in elementary soft topological spaces

Keywords: Soft set, soft element, elementary operations, elementary soft topology, soft base, dense soft set, countable soft space, separable soft space, Lindelöf soft space. The aim of this thesis is to define countability, separability and Lindelöf's properties in elementary soft topological spaces and to examine their basis topological properties. For this purpose, the following studies has been performed. 1. The dense soft set in elementary soft topological spaces has been defined and some examples have been given. 2. The first countable elementary soft topological spaces has been defined, some examples have been given. It proved that the first countable elementary soft topological space has the hereditary property and topological property. 3. The second countable elementary soft topological spaces has been defined. It showed that the second countable elementary soft topological space has the hereditary property and topological property and proved that every soft open covers of each soft subset in a second countable elementary soft topological space have a countable soft sub-cover. Second countable space was compared with first countable space. 4. The concept of separability in elementary soft topological spaces has been defined and some examples have been given. The relationship between separable space and second countable space was examined. It showed that the separable elementary soft topological space has the topological property, but it hasn't hereditary property. 5. Lindelöf's elementary soft space has been defined. The relationship between Lindelöf's space and second countable space was examined. It showed that the elementary soft Lindelöf's space has the topological property. It proved that hereditary property of Lindelöf's elementary soft space is satisfied only for its closed soft subset.