Local T_0 and T_1 constant filter convergence spaces

This thesis consists of five chapters. In the first chapter, there is a literature review. In the second chapter, the concepts of category, functor, topological functor, initial-final lifts, discrete objects, and some necessary theorems and examples about them are given. In the third chapter, constant filter convergence spaces are defined and examples are given. The relationships between constant filter convergence spaces and topological spaces is examined. The category 𝐂𝐨𝐧𝐅𝐂𝐎 (Objects are constant filter convergence spaces and morphisms are continuous maps) is shown topological category. Furthermore, some special objects and morphisms in the 𝐂𝐨𝐧𝐅𝐂𝐎 category are defined. In the fourth chapter, the local T_0, T'_0 and T_1 objects in ConFCO are investigated and simple examples are given as an application of theorems. It is shown that the full subcategories of the category of constant filter convergence spaces consisting of local T_0, T'_0 and T_1 constant filter convergence spaces are hereditary, productive, and co-productive. Furthermore, it is shown the subcategories T_0ConFCO and T_1ConFCO (T'_0ConFCO and ConFCO) of T_1ConFCO are isomorphic categories. In the fifth chapter, the results obtained from from the theorems are brought together, results, evaluations, and suggestions are given