Different authors have defined and studied different types of fuzzy topologies. This thesis aims to investigate and analyze five common forms of fuzzy topology, emphasizing their unique features. This thesis presents a comprehensive study of fuzzy topological spaces, including different types of definitions of fuzzy topologies. basic properties, and continuity of functions in each of those fuzzy topological spaces. This thesis examines, compares, and classifies different types of topological spaces fuzzy and their properties are hidden. We also focus on basic concepts such as open sets, closed sets, neighborhoods, and concentration, with rigorous consideration of the definitions, issues, and evidence they focus on. In this thesis, we compares different types of fuzzy topological spaces and their classified properties. As well as identifying some properties of fuzzy continuous functions for each type, fuzzy topology concepts including the separation axioms, connectedness, compactness and Hausdorffness in the validation of fuzzy topological spaces are introduced.
