On topological ordered spaces

In this thesis, the concept of generalized closed sets defined by N. Levine have been considered as the basis. The answer to the question of when in topological ordered spaces the general closed set and classes of some special closed set built on it coincided has been investigated. Furthermore, some separation axioms which are weaker than T_1 space and stronger than T_0 space have been investigated. This study consists of five chapters. After a brief historical outline has been presented in the introduction, the necessary information and concepts have been given as the basis for the studies in the second chapter. In the third chapter, generalized closed (g-closed) sets have been introduced and the topological properties of the g-closed sets have been characterized. In addition, the relationship between topology and the concept of order has been mentioned. In the fourth chapter, research findings on related closed sets and separation axioms have been indicated and examples have been presented. In the last section, the results obtained have been discussed.