Fuzzy Imbedding Theory and Its Applications

Abstract:

      This paper deals with the imbedding problem in the lattices with a topology. Precisely, we discuss the imbedding problem in L-fuzzy topological space, where L is a fuzzy lattice. Some fundamental results such as the fuzzy unit intezval, Q-nei-ghborhood structure and algebraic properties of union-preserving maps in lattices are collected. A pointwise characterization of fuzzy complete regularity is yielded by means of the Q- neighborhood structures and some algebraic properties of certain class of maps in lattices. The Weil theorem on fuzzy uniformity and the general imbedding theorem in the fuzzy basic cube are established. As applications of the imbedding theorem, a fuzzy version of the well-known Urysohn metrizable theorem and the general theory of the fuzzy Stone-Cech compactification are given.