FUZZY PRETOPOLOGICAL SPACES, AN EXTENSIONAL TOPOLOGICAL EXTENSION OF FTS

The category of fuzzy pretopological spaces is introduced, and it is proved that this category is a well-fibred extensional topological construct, and it is a finally dense extension of the category of fuzzy topological spaces. Moreover this category contains both the category of pretopological spaces and the category of probabilistic neighbourhood spaces as simultaneously bireflective and bicoreflective full subcategories.