Abstract
This paper is on the level decompositions corresponding to the elements in the range of an L-fuzzy topology on a given set and an investigation into the lattice structure of the same. In general, this lattice is not complete and distributive. However, certain necessary and sufficient conditions for it to be modular, distributive, complete and complemented are derived. Atoms and dual atoms of it along with the conditions for their existence are obtained. Certain related properties of it are also discussed here.
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