Characterization of transitivity in L-tolerance spaces by convergence and closure by Gunther Jaeger and T. M. G. Ahsanullah

Journal Article
Publication Work Type
Original Research
Publishing City
Switzerland
Publisher Name
Axioms (MDPI)
Issue Number
268
Volume Number
10
Pages
1 to 16
Publication Abstract

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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