Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory.
Fuzzy topology is one such branch, combining ordered structure with topological structure.
This branch of mathematics, emerged from the background processing fuzziness, and locale theory, proposed from the angle of pure mathematics by the great French mathematician Ehresmann, comprise the two most active aspects of topology on lattice, which affect each other. The monograph can serve as a reference book for mathematicians, researchers, and graduate students working in this branch of mathematics. After an appropriate rearrangements of the chapters and sections, it can also be used as a text for undergraduates. Senior undergraduates, graduate students, and researchers in mathematics and computer science. This will be a very useful reference book for everyone working in this field.