The applications of the universal morphisms of LF-TOP the category of all fuzzy topological spaces

摘要

Finding the universal morphisms for a given category is considered as comprehensive study of the principal properties that this category can achieved. In this work, we build a category of fuzzy topological spaces with respect to Lowen's definition of Fuzzy TOPological space [3], that we denoted LF-TOP. Firstly, we collected universal morphisms of TOP category, listed by Sander Mac Lane [7]. Second, we studied universal morphisms of LF-TOP. We found through this study that the properties of this category are a generalization to the TOP category properties and TOP's universal morphisms are projections of LF-TOP's ones. This shows the power of Lowen's fuzziness effect on the ordinary topological space.