Abstract
Smooth fuzzy topologies are an extension of both crisp topologies and fuzzy topologies, in the sense that not only the objects are fuzzified, but also the axiomatics. In this article, we will complete the proof of the result given in (Chattopadhyay et al., Fuzzy Sets and Systems 49 (1992) 237), stating that the collection of smooth fuzzy topologies, equipped with the pointwise order, is a complete lattice. To this end, we will establish a subbase and base lemma for these by proving that any valuation function can be modified to construct a gradation of openness.
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