An approach to fuzzy frames via fuzzy posets

In this paper, based on a complete Heyting algebra L, we define a fuzzy version of frames, called L-frames. Then we construct an adjunction between the category of stratified L-topological spaces and that of L-locales (the opposite category of L-frames), which is a fuzzy counterpart of the Isbell-adjunction between topological spaces and locales. We also study the corresponding sobriety of stratified L-topologies and spatiality of L-frames and show the dual equivalence between them. (C) 2010 Elsevier B.V. All rights reserved.