Abstract and concrete categories
Abstract and concrete categories
A new approach for fuzzy topology (I)
Fuzzy Sets and Systems
On the sum of L-fuzzy topological spaces
Fuzzy Sets and Systems
L-Fuzzifying topologies as L-topologies
Fuzzy Sets and Systems
On separation axioms in I-fuzzy topological spaces
Fuzzy Sets and Systems
Generated I-fuzzy topological spaces
Fuzzy Sets and Systems
On (L,M)-fuzzy quasi-uniform spaces
Fuzzy Sets and Systems
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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It follows from L-FTOP being topological over SET that there is L-fuzzy topological sum in L-FTOP. In this paper, we use the final topologies constructed in Section 3 of Rodabaugh [Powerset operator foundations of variable-basis fuzzy topology, in: U. Hohle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, the Handbooks of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Boston/Dordrecht/London, 1999, pp. 91-116] to characterize L-fuzzy topological sum internally and establish connections between L-fuzzy topological sum and its factor spaces. We create a functor @w from L-FYS (the category of L-fuzzifying topological space) to L-FTOP and show that @w has a right-adjoint, hence there exists an adjunction from L-FYS to L-FTOP. Moreover @w preserves L-fuzzy topological sums that already exists in both L-FYS and L-FTOP. Finally, we examine certain additivity property of L-fuzzy topological spaces. These results imply that the topological sum in L-FTOP, a necessary consequence of L-FTOP being a topological construct, is now better understood.