Abstract
In this paper, a complete solution to the problem of Stone's repesentation theorem in fuzzy topology is given for a class of completely distributive lattices. Precisely, it is proved that if L is a frame such that 0∈ L is a prime or 1∈ L is a coprime, then the category of distributive lattices is dually equivalent to the category of coherent L -locales and that if L is moreover completely distributive, then the category of distributive lattices is dually equivalent to the category of coherent stratified L -topological spaces.
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