On the order conditions of fuzzy convergence classes

Abstract

By means of the order structure of the related lattice, the LIMINF condition of fuzzy convergence classes is proposed in this paper, which reflects the essential difference between fuzzy convergence classes and ordinary convergence classes. The relationship between the LIMINF condition and two related conditions proposed by Liu and Wang respectively are discussed. The theory of fuzzy convergence classes based on LIMINF condition is established for topological molecular lattices, L-topological spaces (in the sense of Chang or Lowen), weakly induced spaces, and induced spaces.