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A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces. (English) Zbl 1184.54006

Authors’ summary: We study a category of lattice-valued uniform convergence spaces where the lattice is enriched by two algebraic operations. This general setting allows us to view the category of lattice-valued uniform spaces as a reflective subcategory of our category, and the category of probabilistic uniform limit spaces as a coreflective subcategory.

MSC:

54A40 Fuzzy topology
54E15 Uniform structures and generalizations
06F07 Quantales
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
18B30 Categories of topological spaces and continuous mappings (MSC2010)
54B30 Categorical methods in general topology
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