In this paper, we obtain L-fuzzy uniformities induced by Lneighborhood systems and L-fuzzy topologies in complete residuated lattices. Moreover, every N -continuous maps are fuzzy uniformly continuous and every fuzzy continuous maps are fuzzy uniformly continuous.
The aim of this paper is to investigate the relations among the L-fuzzy pre-proximities, L-fuzzy closure operators and L-fuzzy co-topologies in complete residuated lattices. We show that there is a Galois correspondence between the category of separated L-fuzzy closure spaces and that of separated L-fuzzy pre-proximity spaces and we give their examples.
In this paper, we define L-neighborhood spaces and investigated the topological properties of L-fuzzy uniformity in complete residuated lattices. We obtain L-fuzzy topology and L-neighborhood spaces induced by Lfuzzy uniformity. Moreover, we study the relations among L-fuzzy topology, L-neighborhood system and L-fuzzy uniformity.
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