Closure operators in constant filter convergence spaces

Topological categories are used in various areas of mathematics, including geometry, analysis, and algebraic topology. For example, a subset of a topological space is also equipped with a topology. Moreover, the product of two topological spaces is a topological space or the most coarse topology on a set, the indiscrete topology, always exists. Topological categories provide a framework for studying and characterizing these and many other properties of topological spaces systematically. In this thesis, the ConFCO category, whose objects are constant filter convergence spaces and morphisms are continuous functions between these spaces, is examined. In ConFCO, the axis maps and the closure and strong closure of a set are investigated. Subsequently, it is shown whether closed (strongly closed) sets are closed (strongly closed) under finite and arbitrary intersections and unions. Afterwards, some closure operators (cl,scl,Q,sQ) in the ConFCO category are characterized. The idempotent, (weak) hereditary, multiplicative, and additive states of these closure operators are examined. Additionally, the 〖ConFCO〗_ic subcategories for i=0,1,2 formed by closure operators are investigated and the relationships between them are shown. Hence, by using closure operators, each of the T_i constant filter convergence spaces for i=0,1 has been characterized. Subsequently, it is determined that the 〖ConFCO〗_ic categories are the epireflective subcategories of ConFCO. Finally, the results obtained in this thesis study are compared with the results in some known topological categories.