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Reflectivity and coreflectivity between the category of topological spaces, the category of topological fuzzes and the category of topological molecular lattices. (Chinese. English summary) Zbl 1007.54007

Summary: It is shown that the category Top of topological spaces is a reflective and coreflective full subcategory of the category TML of topological molecular lattices and the category TopFuzz of topological fuzzes respectively; it is also shown that TopFuzz is a reflective and coreflective (nonfull) subcategory of TML, the integral relations between Top, TopFuzz and TML are first exploited.

MSC:

54A40 Fuzzy topology
54H12 Topological lattices, etc. (topological aspects)
06B35 Continuous lattices and posets, applications
54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
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