L-structure and its application (Q1108605)

This paper consists mainly of two more or less independent parts. The first part regards a natural generalization of Chang fuzzy topological spaces to so-called L-structures. Zadeh's set of membership degrees [0,1] is replaced by a complete, completely distributive lattice L provided with an order-reversing involution and a smallest as well as a greatest element. For every point x from a universe X, a so-called quasi- neighbourhood system \({\mathcal L}(x)\) is defined. This system is used to define a fuzzy interior and a fuzzy closure operator on the class of all L-fuzzy sets on X. ByAut(\({\mathbb{Q}})\)-orbit in \(\beta\) \({\mathbb{Q}}-{\mathbb{Q}}\) is uncountable. He also gives a number of other results of a similar nature, including some derived from a quite different proof of the separability of \(\beta\) \({\mathbb{Q}}-{\mathbb{Q}}\).