Separation axioms, closedness, connectedness, sober object and compactness in the category of constant limit spaces

In this thesis, firstly, it is shown that ConLim category, whose objects are constant limit spaces and whose morphisms are continuous maps, is topological on Set. Afterwards, T_i objects for both local and general i = 0,1 were characterized and full subcategories as T_i ConLim were obtained. Then, closed and strongly closed objects in this category were determined, and theorems known in General Topology such as Tietze Extension Theorem and Urysohn's Lemma were expressed and proved in ConLim. Finally, connected, disconnected, sober and compact objects in this topological category were characterized and investigated the relationships between them. In addition, at the end of each section of the paper, our results for ConLim were compared with the results in other topological categories.