Three New Weaker Notions of Fuzzy Open Sets and Related Covering Conceps - Al Ghour, Samer H. (Kuwait Journal of Science, 2017)
A subset A of an ordinary topological space (X,T) is ω-open Hdeib1 (resp. N-open alomari3) if for each x∈A, there exists U∈T such that x∈U and U-A is countable (resp. finite). In this work, we extend ω-open and N-open notions to include L-topological spaces, where L is an F-lattice, and we introduce a third notion of L-sets weaker than both of them. For a given L-topological space, the new notions give us three new finer L-topological spaces, which can help us to increase our understanding of this L-topological space. By means of these new notions in L-topological spaces, several types Chang’s compactness, and Wong’s Lindelöfness will be introduced. We make many comparisons between the new notions, and between these notions and some other related concepts. Several characterizations of the new concepts are given and two characterizations of Wong’s Lindelöfness concept are given.