Lowen spaces (Q1970948)

An \(L\)-topological space \((L^X,\delta)\), where \(L\) is a completely distributive complete lattice, is said to be a Lowen space (this notion coincides with Lowen's notion of fuzzy neighborhood space [\textit{R. Lowen}, Fuzzy Sets Syst. 7, No. 2, 165-189 (1982; Zbl 0487.54008)] when \(L=[0,1]\)) if \(\delta\) has a base \(\beta\subset\{_aU \mid a\in L\), \(U\subset X\}\). The authors prove several characterizations of Lowen spaces, and thus show that the category of Lowen spaces is isomorphic to the category of \(L\)-fuzzifying topological spaces.