Characterization of Transitivity in L-Tolerance Spaces by Convergence and Closure

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.

Keywords

• L-tolerance space
• L-pretolerance convergence space
• L-tolerance convergence space
• L-closure function
• L-equivalence relation
• L-valued set