In this note, we continue the works in the paper [Some properties of L-fuzzy approximation spaces on bounded integral residuated lattices", Information Sciences, 278, 110-126, 2014]. For a complete involutive residuated lattice, we show that the L-fuzzy topologies generated by a reflexive and transitive L-relation satisfy (TC)_L or (TC)_R axioms and the L-relations induced by two L-fuzzy topologies, which are generated by a reflexive and transitive L-relation, are all the original L-relation; and give out some conditions such that the L-fuzzy topologies generated by two L-relations, which are induced by an L-fuzzy topology, are all the original L-fuzzy topology.
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