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Lattice-valued coarse structures
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DOI：10.1016/j.fss.2024.109175.png)
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Abstract
En 中文
Based on a complete residuated lattice L , we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of L-entourages and L-(quasi, semi)-coarse structures and study the maps between L-coarse spaces. Secondly, we provide some examples of L-coarse structures from the aspects of L-metrics, L-relations and L-hyperstructures. Thirdly, we introduce the notion of L-ball structures to characterize L-coarse structures. Finally, we establish the relationship among L-entourage spaces, L-quasi-coarse spaces, L-semi-coarse spaces and Lcoarse spaces in a categorical viewpoint.
Keywords:
L-coarse structure
L-bornology
L-bornologous map
L-ball structure
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