Fuzzy functions and an extension of the category \(L\)-Top of Chang-Goguen \(L\)-topological spaces (Q2782227)

This paper generalizes and continues previous work by the author. New definitions and properties about the category FSET\((L)\) are introduced, which are used as the ground category for the \(L\)-fuzzy category FTOP\((L)\). The objects of this category are Chang-Goguen \(L\)-topological spaces, whose morphisms are certain fuzzy functions, i.e. morphisms from FSET\((L)\). NEWLINENEWLINENEWLINELater, the category FTOP\((L)\) is studied, in particular, the author shows that the top frame \(\text{FTOP}(L)^\top\) is a topological category in Herrlich's sense over the top frame FSET\((L)^\top\) of the fuzzy category FSET\((L)\). NEWLINENEWLINENEWLINESome topological properties are given of \(L\)-valued \(L\)-topological spaces with respect to fuzzy functions. For example, if L is an \(MV\)-algebra, one can characterize compactness of systems of closed \(L\)-sets by applying De Morgan laws.NEWLINENEWLINEFor the entire collection see [Zbl 0983.00046].