A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces

Authors:
Andrew Craig;Gunther Jäger
Affiliations:
Department of Mathematics, Rhodes University, 6140 Grahamstown, South Africa;Department of Statistics, Rhodes University, 6140 Grahamstown, South Africa
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

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.