Topology, fuzzy transform, F-transform

In this paper, we discuss the relationship betweenthe direct lattice-based F-transform and L-fuzzy pretopology. The importance of fuzzy pretopological spaces follows from the fact that they are dense extensions of fuzzy topological spaces, and thecorresponding category contains both Top and the category PNeigh of probabilistic neighbourhood spaces. We show that every direct F#-transform uniquely determines an L-fuzzy pretopologyand discuss the opposite correspondence.In between, some categorical results have been established. Further, some new F-transform theoretic results are studied.