Characterization of transitivity in L-tolerance spaces by convergence and closure by Gunther Jaeger and T. M. G. Ahsanullah
We show that the category of quantale-valued tolerance spaces is isomorphic to a category of quantale-valued convergence spaces. We define suitable quantale-valued closure functions and use them to characterize transitivity axioms. Furthermore, transitivity is characterized by convergence and diagonal axioms. Quantale-valued tolerance relations compatible with group structures are also characterized by convergence and it is shown that they are transitive.
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Starting with the category of probabilistic approach groups, we show that the category of approach groups can be embedded into the category of probabilistic approach groups as a bicoreflective…
Starting with an approximation space as the underlying structure, we
look at the rough uniformity of a topological rough group. Next, taking L as a
complete residuated lattice, we…