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Extensional \(L\)-fuzzy Q-convergence structures. (English) Zbl 1366.54006

Summary: In this paper, the concept of extensional \(L\)-fuzzy Q-convergence structures is proposed. It is shown that there is an adjunction between the category of extensional \(L\)-fuzzy topological spaces and the category of extensional \(L\)-fuzzy topological spaces. In particular, the category of extensional \(L\)-fuzzy topological spaces can be embedded in the category of extensional \(L\)-fuzzy Q-convergence spaces as a reflective subcategory. Also, the notion of topological extensional \(L\)-fuzzy Q-convergence spaces is introduced and the resulting category is shown to be isomorphic to the category of extensional \(L\)-fuzzy topological spaces.

MSC:

54A40 Fuzzy topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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