Study of Certain Topics in Fuzzy Supra Topological Space

Abstract

American Mathematician Lotfi A. Zadeh in 1965 first introduced the concept of fuzzy set. He interpreted a fuzzy set on a set as a mapping from the set into the unit interval I= [0, 1], which is a generalization of the characteristic function of the set. Many mathematicians throughout the world used this set to fuzzify different areas of mathematics. Fuzzy supra topology is one of the outcomes of such fuzzification of the usual topology. In this thesis, we have studied and have introduced several results on fuzzy supra topological spaces. At first we have discussed the standard definitions and properties of fuzzy supra R0 and R1 topological spaces, which are found in the literatures. Then we have introduced some new definitions and properties for these spaces. We have also studied the Fuzzy supra T0, T1 , T2 and Fuzzy supra regular topological spaces and obtained the following properties, such as, Good extension, Initial, Reciprocal, Productivity, Hereditary and Homeomorphism, etc. Moreover we have discussed compactness of Fuzzy Supra Topological Spaces and have proposed some new definitions, theorems and proofs.