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Abstract The concept of fuzzy subsets , introduced by Zadeh [41] in 1965 , played an important role in applications and in such mathematical theories as Logic and Topology . In 1968, Chang [3] used this concept to introduce the concept of fuzzy topological spaces. Subsequently. Wong 138, 391, Lowen 1151 , and others extended some basic concepts from general topology to fuzzy subsets and developed a theory of fuzzy topological spaces . Ln 1982, Lowen [19], introduced the concept of fuzzy neighbourhood spaces (FNS,for short ), where they are a special type of fuzzy topological spaces . This concept has been developed by several authors ( e.g. [26] ). Ln 1993, Nehad N. Morsi [28], introduced the notion of a core theory, simultaneously for general topology and for fuzzy topology . He generalized the theory of the Scott topology on a partially ordered set, as a special instance of core theory from general topology . |