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The fuzzy set gives us a framework that is wider than that of a classical set idea. The abilities of numerous mathematical systems emphasize the outcomes of ordered form that are some times superior. Fuzzy topology is one such branch which combines ordered shape with topological form. This branch of arithmetic which emerged from the historical past processing fuzziness. Fuzzy set theory provides a significantly newer paradigm in modeling and reasoning with uncertainty. I express my heartiest thanks to my esteemed Guide and Supervisor, Dr. B. Amudhambigai. Her inspiring and inimitable encouragements, ingenious help, invaluable and innovative suggestions and constructive criticism helped me a lot.