Local Hausdorff and pre-Hausdorff constant filter convergence spaces

This thesis consists of five chapters and the purpose of this thesis is as follows: (1) To characterize local pre-Hausdorff(preT_2) and Hausdorff(T_2) constant filter convergence spaces and investigate the relationships among these various forms, (2) To research that these full subcategories of the category of constant filter convergence spaces consisting of local preT_2 and local T_2 constant filter convergence spaces are hereditary, productive, and co-productive, (3) To show the full subcategories KT_2(ConFCO) and preT_2(ConFCO) of ConFCO are isomorphic categories. In the first and second chapters, the concepts of category, fanctor, topological fanctor, initial-final lifts, discrete objects, and some necessary theorems are given. In the third chapter, constant filter convergence spaces are defined and examples are given. Then, the relationships among constant filter convergence spaces and topological spaces are determined. The category ConFCO are shown a normalized topological category. Then, some special objects and morphisms in the ConFCO category are characterized. In the fourth chapter, the axis maps at point p and separation properties in topological categories are given. Furthermore local T_0 objects in ConFCO are given and these objects used to describe local preT_2 and local T_2 objects in ConFCO. It is shown that the full subcategories of consisting of local preT_2 and local T_2 constant filter convergence spaces (preT_2(ConFCO), preT'_2(ConFCO), T_2(ConFCO), T'_2(ConFCO), and KT_2(ConFCO)) are hereditary, productive, and co-productive. Finally, it is present that the subcategories KT2(ConFCO) and preT_2(ConFCO) are isomorphic categories. In the fifty chapter, the results obtained from the theorems are brought together, evaluations and suggestions are given.